When I started following this discussion, my expectation (like many others here) was the EyeTV iOS app would be ported to tvOS. It's good to see you are still discussing this as an option.
If possible, the ATV4 app should have the same features as the EyeTV app with the following additions:
The tvOS app would need to play EyeTV recordings without preparing/converting to H.264, as is required with the iOS app.
Nice to have:
Adjustable playback speed (.5x,1x,1.5x, etc)
FastForward/Rewind setting (10sec,30sec,60sec, etc)
There are several apps already available with these capabilities (Elmedia Player, Infuse, VLC, etc). However, none of them handle EyeTV recordings very well. I think a port of the existing EyeTV app would be a great solution.