Dude. I have a main switch that has cables running all over my house. I've got a switch at EVERY wall plate where I ran a cable. I'm an idiot and didn't think my setup all the way through, but they get the job done and are cheap. I've used the exact ones
@NINaudio linked and all you'll need to do is get a switch. Take your RJ45 wall plate, plug a cable into it. Plug that same cable into port 1 of your switch. and stick the switch to the back of the TV so you can plug in other stuff. ATV can be stuck to the back as well.
Trust me. Your issue is way easier to solve than you think. No more drywall cutting I promise.