I added a small (19") TV to the rear room of my 23SS. It's not the exact same layout, but similar principle should apply.
The wall mount of the TV had only 2 screws, and no structure in the wall where I wanted it. So I used a leftover piece of Pergo laminate flooring as strapping. I made it go from corner to corner, so I could pick up the structural supports in the corners. And a couple more screws in the middle, including the wall mount screws.
It doesn't look bad, and the TV is Solidly in there!!
2013 Rockwood Roo 23SS
2003 Ford F150 4.6L V8