Final (almost) proposal:
Given the following WebUI settings:

The http://tvh:9981/api/tvhlog/subsystem/grid produces the following output:
{
    "entries": [
        {
            "id": 1,
            "subsystem": "START",
            "description": "START",
            "trace": false,
            "debug": true     <=====
        },
        {
            "id": 2,
            "subsystem": "STOP",
            "description": "STOP",
            "trace": true,     <=====
            "debug": false
        },
        {
            "id": 3,
            "subsystem": "CRASH",
            "description": "CRASH",
            "trace": false,
            "debug": true     <=====
        },
        {
            "id": 4,
            "subsystem": "main",
            "description": "Main",
            "trace": true,     <=====
            "debug": false
        },
        {
            "id": 5,
            "subsystem": "tprof",
            "description": "Time profiling",
            "trace": true,     <=====
            "debug": true     <=====
        },
        {
            "id": 6,
            "subsystem": "qprof",
            "description": "Queue profiling",
            "trace": false,
            "debug": false
        },
        {
            "id": 7,
            "subsystem": "CPU",
            "description": "CPU",
            "trace": false,
            "debug": false
        },
        {
            "id": 8,
            "subsystem": "thread",
            "description": "Thread",
            "trace": false,
            "debug": false
        },
        {
            "id": 9,
            "subsystem": "tvhpoll",
            "description": "Poll multiplexer",
            "trace": false,
            "debug": false
        },
        {
            "id": 10,
            "subsystem": "time",
            "description": "Time",
            "trace": false,
            "debug": false
        },
        {
            "id": 11,
            "subsystem": "spawn",
            "description": "Spawn",
            "trace": false,
            "debug": false
        },
        {
            "id": 12,
            "subsystem": "fsmonitor",
            "description": "Filesystem monitor",
            "trace": false,
            "debug": false
        },
        {
            "id": 13,
            "subsystem": "lock",
            "description": "Locking",
            "trace": false,
            "debug": false
        },
        {
            "id": 14,
            "subsystem": "uuid",
            "description": "UUID",
            "trace": false,
            "debug": false
        },
        {
            "id": 15,
            "subsystem": "idnode",
            "description": "Node subsystem",
            "trace": false,
            "debug": false
        },
        {
            "id": 16,
            "subsystem": "url",
            "description": "URL",
            "trace": false,
            "debug": false
        },
        {
            "id": 17,
            "subsystem": "tcp",
            "description": "TCP Protocol",
            "trace": false,
            "debug": false
        },
        {
            "id": 18,
            "subsystem": "rtsp",
            "description": "RTSP Protocol",
            "trace": false,
            "debug": false
        },
        {
            "id": 19,
            "subsystem": "upnp",
            "description": "UPnP Protocol",
            "trace": false,
            "debug": false
        },
        {
            "id": 20,
            "subsystem": "settings",
            "description": "Settings",
            "trace": false,
            "debug": false
        },
        {
            "id": 21,
            "subsystem": "config",
            "description": "Configuration",
            "trace": false,
            "debug": false
        },
        {
            "id": 22,
            "subsystem": "access",
            "description": "Access (ACL)",
            "trace": false,
            "debug": false
        },
        {
            "id": 23,
            "subsystem": "cron",
            "description": "Cron",
            "trace": false,
            "debug": false
        },
        {
            "id": 24,
            "subsystem": "dbus",
            "description": "DBUS",
            "trace": false,
            "debug": false
        },
        {
            "id": 25,
            "subsystem": "avahi",
            "description": "Avahi",
            "trace": false,
            "debug": false
        },
        {
            "id": 26,
            "subsystem": "bonjour",
            "description": "Bonjour",
            "trace": false,
            "debug": false
        },
        {
            "id": 27,
            "subsystem": "api",
            "description": "API",
            "trace": false,
            "debug": false
        },
        {
            "id": 28,
            "subsystem": "http",
            "description": "HTTP Server",
            "trace": false,
            "debug": false
        },
        {
            "id": 29,
            "subsystem": "httpc",
            "description": "HTTP Client",
            "trace": false,
            "debug": false
        },
        {
            "id": 30,
            "subsystem": "htsp",
            "description": "HTSP Server",
            "trace": false,
            "debug": false
        },
        {
            "id": 31,
            "subsystem": "htsp-sub",
            "description": "HTSP Subscription",
            "trace": false,
            "debug": false
        },
        {
            "id": 32,
            "subsystem": "htsp-req",
            "description": "HTSP Request",
            "trace": false,
            "debug": false
        },
        {
            "id": 33,
            "subsystem": "htsp-ans",
            "description": "HTSP Answer",
            "trace": false,
            "debug": false
        },
        {
            "id": 34,
            "subsystem": "imagecache",
            "description": "Image Cache",
            "trace": false,
            "debug": false
        },
        {
            "id": 35,
            "subsystem": "tbl",
            "description": "DVB SI Tables",
            "trace": false,
            "debug": false
        },
        {
            "id": 36,
            "subsystem": "tbl-base",
            "description": "Base DVB SI Tables (PAT,CAT,PMT,SDT etc.)",
            "trace": false,
            "debug": false
        },
        {
            "id": 37,
            "subsystem": "tbl-csa",
            "description": "DVB CSA (descrambling) Tables",
            "trace": false,
            "debug": false
        },
        {
            "id": 38,
            "subsystem": "tbl-eit",
            "description": "DVB EPG Tables",
            "trace": false,
            "debug": false
        },
        {
            "id": 39,
            "subsystem": "tbl-time",
            "description": "DVB Time Tables",
            "trace": false,
            "debug": false
        },
        {
            "id": 40,
            "subsystem": "tbl-atsc",
            "description": "ATSC SI Tables",
            "trace": false,
            "debug": false
        },
        {
            "id": 41,
            "subsystem": "tbl-pass",
            "description": "Passthru Muxer SI Tables",
            "trace": false,
            "debug": false
        },
        {
            "id": 42,
            "subsystem": "tbl-satip",
            "description": "SAT>IP Server SI Tables",
            "trace": false,
            "debug": false
        },
        {
            "id": 43,
            "subsystem": "fastscan",
            "description": "Fastscan DVB",
            "trace": false,
            "debug": false
        },
        {
            "id": 44,
            "subsystem": "pcr",
            "description": "PCR Clocks",
            "trace": false,
            "debug": false
        },
        {
            "id": 45,
            "subsystem": "parser",
            "description": "MPEG-TS Parser",
            "trace": false,
            "debug": false
        },
        {
            "id": 46,
            "subsystem": "TS",
            "description": "Transport Stream",
            "trace": false,
            "debug": false
        },
        {
            "id": 47,
            "subsystem": "globalheaders",
            "description": "Global Headers",
            "trace": false,
            "debug": false
        },
        {
            "id": 48,
            "subsystem": "tsfix",
            "description": "Time Stamp Fix",
            "trace": false,
            "debug": false
        },
        {
            "id": 49,
            "subsystem": "hevc",
            "description": "HEVC - H.265",
            "trace": false,
            "debug": false
        },
        {
            "id": 50,
            "subsystem": "muxer",
            "description": "Muxer",
            "trace": false,
            "debug": false
        },
        {
            "id": 51,
            "subsystem": "pass",
            "description": "Pass-thru muxer",
            "trace": false,
            "debug": false
        },
        {
            "id": 52,
            "subsystem": "audioes",
            "description": "Audioes muxer",
            "trace": false,
            "debug": false
        },
        {
            "id": 53,
            "subsystem": "mkv",
            "description": "Matroska muxer",
            "trace": false,
            "debug": false
        },
        {
            "id": 54,
            "subsystem": "service",
            "description": "Service",
            "trace": false,
            "debug": false
        },
        {
            "id": 55,
            "subsystem": "channel",
            "description": "Channel",
            "trace": false,
            "debug": false
        },
        {
            "id": 56,
            "subsystem": "subscription",
            "description": "Subscription",
            "trace": false,
            "debug": false
        },
        {
            "id": 57,
            "subsystem": "service-mapper",
            "description": "Service Mapper",
            "trace": false,
            "debug": false
        },
        {
            "id": 58,
            "subsystem": "bouquet",
            "description": "Bouquet",
            "trace": false,
            "debug": false
        },
        {
            "id": 59,
            "subsystem": "esfilter",
            "description": "Elementary Stream Filter",
            "trace": false,
            "debug": false
        },
        {
            "id": 60,
            "subsystem": "profile",
            "description": "Streaming Profile",
            "trace": false,
            "debug": false
        },
        {
            "id": 61,
            "subsystem": "descrambler",
            "description": "Descrambler",
            "trace": false,
            "debug": false
        },
        {
            "id": 62,
            "subsystem": "descrambler-emm",
            "description": "Descrambler EMM",
            "trace": false,
            "debug": false
        },
        {
            "id": 63,
            "subsystem": "caclient",
            "description": "CA (descrambling) Client",
            "trace": false,
            "debug": false
        },
        {
            "id": 64,
            "subsystem": "csa",
            "description": "CSA (descrambling)",
            "trace": false,
            "debug": false
        },
        {
            "id": 65,
            "subsystem": "capmt",
            "description": "CAPMT CA Client",
            "trace": false,
            "debug": false
        },
        {
            "id": 66,
            "subsystem": "cwc",
            "description": "CWC CA Client",
            "trace": false,
            "debug": false
        },
        {
            "id": 67,
            "subsystem": "cccam",
            "description": "CWC CCCam Client",
            "trace": false,
            "debug": false
        },
        {
            "id": 68,
            "subsystem": "dvbcam",
            "description": "DVB CAM Client",
            "trace": false,
            "debug": false
        },
        {
            "id": 69,
            "subsystem": "dvr",
            "description": "Digital Video Recorder",
            "trace": false,
            "debug": false
        },
        {
            "id": 70,
            "subsystem": "dvr-inotify",
            "description": "DVR Inotify",
            "trace": false,
            "debug": false
        },
        {
            "id": 71,
            "subsystem": "epg",
            "description": "Electronic Program Guide",
            "trace": false,
            "debug": false
        },
        {
            "id": 72,
            "subsystem": "epgdb",
            "description": "EPG Database",
            "trace": false,
            "debug": false
        },
        {
            "id": 73,
            "subsystem": "epggrab",
            "description": "EPG Grabber",
            "trace": false,
            "debug": false
        },
        {
            "id": 74,
            "subsystem": "charset",
            "description": "Charset",
            "trace": false,
            "debug": false
        },
        {
            "id": 75,
            "subsystem": "dvb",
            "description": "DVB",
            "trace": false,
            "debug": false
        },
        {
            "id": 76,
            "subsystem": "mpegts",
            "description": "MPEG-TS",
            "trace": false,
            "debug": false
        },
        {
            "id": 77,
            "subsystem": "muxsched",
            "description": "Mux Scheduler",
            "trace": false,
            "debug": false
        },
        {
            "id": 78,
            "subsystem": "libav",
            "description": "libav / ffmpeg",
            "trace": false,
            "debug": false
        },
        {
            "id": 79,
            "subsystem": "transcode",
            "description": "Transcode",
            "trace": false,
            "debug": false
        },
        {
            "id": 80,
            "subsystem": "iptv",
            "description": "IPTV",
            "trace": false,
            "debug": false
        },
        {
            "id": 81,
            "subsystem": "iptv-pcr",
            "description": "IPTV PCR",
            "trace": false,
            "debug": false
        },
        {
            "id": 82,
            "subsystem": "iptv-sub",
            "description": "IPTV Subcription",
            "trace": false,
            "debug": false
        },
        {
            "id": 83,
            "subsystem": "linuxdvb",
            "description": "LinuxDVB Input",
            "trace": false,
            "debug": false
        },
        {
            "id": 84,
            "subsystem": "diseqc",
            "description": "DiseqC",
            "trace": false,
            "debug": false
        },
        {
            "id": 85,
            "subsystem": "en50221",
            "description": "CI Module",
            "trace": false,
            "debug": false
        },
        {
            "id": 86,
            "subsystem": "en50494",
            "description": "Unicable (EN50494)",
            "trace": false,
            "debug": false
        },
        {
            "id": 87,
            "subsystem": "satip",
            "description": "SAT>IP Client",
            "trace": false,
            "debug": false
        },
        {
            "id": 88,
            "subsystem": "satips",
            "description": "SAT>IP Server",
            "trace": false,
            "debug": false
        },
        {
            "id": 89,
            "subsystem": "tvhdhomerun",
            "description": "TVHDHomeRun Client",
            "trace": false,
            "debug": false
        },
        {
            "id": 90,
            "subsystem": "psip",
            "description": "ATSC PSIP EPG",
            "trace": false,
            "debug": false
        },
        {
            "id": 91,
            "subsystem": "opentv",
            "description": "OpenTV EPG",
            "trace": false,
            "debug": false
        },
        {
            "id": 92,
            "subsystem": "pyepg",
            "description": "PyEPG Import",
            "trace": false,
            "debug": false
        },
        {
            "id": 93,
            "subsystem": "xmltv",
            "description": "XMLTV EPG Import",
            "trace": false,
            "debug": false
        },
        {
            "id": 94,
            "subsystem": "webui",
            "description": "Web User Interface",
            "trace": false,
            "debug": false
        },
        {
            "id": 95,
            "subsystem": "timeshift",
            "description": "Timeshift",
            "trace": false,
            "debug": false
        },
        {
            "id": 96,
            "subsystem": "scanfile",
            "description": "Scanfile",
            "trace": false,
            "debug": false
        },
        {
            "id": 97,
            "subsystem": "tsfile",
            "description": "MPEG-TS File",
            "trace": false,
            "debug": false
        },
        {
            "id": 98,
            "subsystem": "tsdebug",
            "description": "MPEG-TS Input Debug",
            "trace": false,
            "debug": false
        },
        {
            "id": 99,
            "subsystem": "codec",
            "description": "Codec",
            "trace": false,
            "debug": false
        },
        {
            "id": 100,
            "subsystem": "vaapi",
            "description": "VA-API",
            "trace": false,
            "debug": false
        },
        {
            "id": 101,
            "subsystem": "ddci",
            "description": "DD-CI",
            "trace": false,
            "debug": false
        },
        {
            "id": 102,
            "subsystem": "udp",
            "description": "UDP Streamer",
            "trace": false,
            "debug": false
        },
        {
            "id": 103,
            "subsystem": "ratinglabels",
            "description": "Rating Labels",
            "trace": false,
            "debug": false
        }
    ],
    "totalCount": 103
}
I may also add a traceCount and debugCount at the end too.  This will help to more easily detect when 'all' is selected instead of individual subsystems.
Maybe in the future this API module could be developed further, such as, http://tvh:9981/api/tvhlog/subsystem/save to set the trace/debug subsystems by index rather than name.  For now, the output can be used to build a concatenated string of subsystems to pass to the existing API.