Only thing with Steam Link and TV gaming is KB and Mouse and 1080p 60hz, would much prefer a monitor but I wont have the room and having everything hidden away is appealing
If I make the move to a smaller case that fit in a TV cab will I just need to change the mobo and case IE how many ITX cases take full size gpus? need to read into it a bit more
Steam Link supports KB and Mouse and runs at 1080p 60fps - unless you're suggesting that's part of the problem

Don't get me wrong, it's not ideal, but you can pick up a steam link for £15 during sales. It's a cheap solution just to try.
A small form factor PC is obviously another solution, just costs more, but totally doable. Other option is just standard PC case hidden as best you can behind/in the TV unit or nearby cupboard.