I have been doing exactly as you propose for the last 15 years. It works great.

I have a bike-tite (like you show) bolted to a 1" X 6" x 3'. I previously had a Ford Explorer with loopy pile carpet, so I attached hook velcro to the bottom of the board to hold it in place.

Now I have a Toyota Sequoia and the carpet isn't as loopy. I just take out the third row passenger seat, tumble the rear passenger seat forward and stick one end of the 1 X 6 under a basket of emergency stuff I have to carry. It holds everything in place just great.

I usually just carry one bike, so I had to deal with the problem in a slightly different way than you have to. If I have to carry more bikes, I use my hitch rack.

Just be careful of the roof liner. My bike in the Explorer was a tight fit, and eventually the roof liner got torn up.

Enjoy!