Setup to use the xbox (one and 360) in a different room

Hello there, fellows.

I looked around the forum, and didn't find anything about it, so I thought I'd ask here. Excuse me if this is a repeat.

So, when I reformed my house some six years ago, I prepared a spot to place my consoles, and used a denon receiver to distribute their signals all around the house, from the tv room, to the bedroom, to the living room. This works great, and I can send my
consoles signal, wired, in 4k, all around the house.

My home is not too big, and in theory, the controller signals should reach everywhere. But they don't. I'm guessing that some of my mirrors, and some metal in the construction, blocks the signal.

I tried to look for ways to extend the signal, but never found any really consistent way I could do it. So eventually I gave up and decided that using that expensive setup to distribute the signal was a waste of money.

But now, with game streaming, I thought maybe I could make a workaround? Maybe, set up the app on my tablet, control it technically through remote play, with the controller linked to the tablet, but send the audio and video through my wired setup
in order not to loose signal quality.

I guess my question is: Would something like that work? I mean, during remote play, do the console even generate image? If so, does it keep the quality of audio and video?

In the end, I'd probably try, but I figured I could ask here before I go through the trouble. Maybe there is some really obvious wrong thing I'm not seeing, maybe it's a tried and true solution. Maybe I even get new ideas on ow to extend the controller reach
in some other way.

Well, that's it. Thanks in advance for any given help.

:)