A BFG KM2 will lay flat on the floor and can be strapped down. Leaves room n the side for first aid bag, small air compressor, tool bag and recovery bag. Chairs lay across the top. I made my own net to cover everything once it is packed.
I looked at mounting the tire in the same manner as done by the OP but did not want to run with the rear seat partially folded down. I keep the Hi-Lift, shovel, and ax under the rear seats and that does not work with the seat folded down.
Excellent mod if you don't mind the seat down. Another bar dropped down to the seat mount would stabilize the mounting bracket and eliminate the need for the strap. If you do use a strap, get a big heavy duty ratchet strap that you can use to remount a tire on your rim. Two birds, one stone.....
"Old age and treachery will overcome youth and skill", Bob Arnett