HEVC x265 works, but...
... only when I upgraded to the latest ffmpeg.exe manually. The reason I did so was because of ffmpeg faulting to the event viewer on my server machine. The manual update fixed that problem. (see the link to update ffmpeg on the Serviio wiki)
Not perfect, though. A 19 min 24 second test file .mkv shows as only 4 min 12 seconds duration in Serviio, but it does play all the way to the end of the 20 minute episode despite the stated time limit.
However, fast forward and resume are not working as of yet for this video stream. Fast forward still works fine on regular file types.
But... at least it plays all the way through if I just don't touch it. If I have to restart it, it does not resume.
HEVC benefits are drastically improved quality and very small file size (a typical HEVC is 345 Kbps and is perfect quality and size smaller than even a converted/compressed file, whereas the approx 452Kbps I usually get after manual compression is nowhere near perfect quality), but since the controls are not yet worked out, it is not a perfect solution, for now.
(Using latest Serviio 1.6)