I have to say that from your viewing distance you will not benefit from 4k over 1080p with screen sizes that will fit in the space.
They are replacing a tv that has nothing wrong with it with a 4K model, I guess I was really saying keep the tv you haveIt's a moot point as you can't buy any "good" 1080P TVs anymore.
It's a moot point as you can't buy any "good" 1080P TVs anymore.
If you can't fit a bigger TV in there maybe get a bracket so the TV is in front of the shelves.