The latest Intel chips work well with vaapi gpu encoding and latest tvheadend has built in codec profile for encoding. Not sure how many streams you'll be able to do at once.
I believe they were also working on NVENC for newer nvidia cards, I don't see the codecs in mine, but I probably didn't compile in nvenc support or have the header files available on my system to do so.
My mobo is an embedded bay trail quad core cpu that cost about $60 or $70US when new. I can transcode 1080 mpeg2 to 1080 h.264 at 2.75x faster than realtime. SD streams are maybe 6-7x. I forget off the top of my head.