Just for reference, Here's my log when tuning to a channel, watching a couple of seconds, then stopping using the internal viewer.
2017-11-09 02:22:17.138 xmltv: xmltv: broadcasts tot=68145 new=10723 mod=10772
2017-11-09 06:07:28.142 mpegts: 545.028MHz in ATSC-T Network - tuning on HDHomeRun ATSC-T Tuner #0 (192.168.222.88)
2017-11-09 06:07:28.142 tvhdhomerun: tuning to auto:545028615
2017-11-09 06:07:28.262 subscription: 0008: "HTTP" subscribing on channel "WLKY-HD", weight: 100, adapter: "HDHomeRun ATSC-T Tuner #0 (192.168.222.88)", network: "ATSC-T Network", mux: "545.028MHz", service: "WLKY-HD", profile="webtv-vp8-vorbis-webm", hostname="127.0.0.1", username="jfath", client="Mozilla/5.0 (X11; Ubuntu; Linux x86_64; rv:56.0) Gecko/20100101 Firefox/56.0"
2017-11-09 06:07:28.612 transcode: 0002: 1:H264 1280x540 ==> VP8 910x384 (libvpx)
2017-11-09 06:07:28.612 transcode: 0002: 2:AC3 ==> VORBIS (libvorbis)
2017-11-09 06:07:29.279 TS: ATSC-T Network/545.028MHz/WLKY-HD: AC3
#52 Continuity counter error (total 1)
2017-11-09 06:07:29.280 TS: ATSC-T Network/545.028MHz/WLKY-HD: H264
#49 Continuity counter error (total 1)
2017-11-09 06:07:29.331 tsfix: The timediff for AC3 is big (810296), using current dts
2017-11-09 06:07:29.378 libav: v1.6.1
2017-11-09 06:07:29.384 tsfix: transport stream AC3, DTS discontinuity. DTS = 940320, last = 8640
2017-11-09 06:07:29.384 transcode: 0002: Detected framedrop in audio
2017-11-09 06:07:49.676 subscription: 0008: "HTTP" unsubscribing from "WLKY-HD", hostname="127.0.0.1", username="jfath", client="Mozilla/5.0 (X11; Ubuntu; Linux x86_64; rv:56.0) Gecko/20100101 Firefox/56.0"
2017-11-09 06:07:49.683 libav: 41 frames left in the queue on closing
This is with an HDHomeRun Extend US version which is set to mobile transcode profile, so the video comes in as h.264.
It looks like Tvheadend is tuning a reasonable frequency for your channel 39, but then doesn't get the data stream expected. Which pre-defined muxes did you choose when setting up your network? Can you set your Extend for mobile transcode profile just to see if it makes a difference?