OP, I made a little spin on your idea:
I needed to be able to at least maintain some of my rear seat, at least enough to have one person sit in the back so I only use the larger portion of the seat for my dog-transport mod. I also didn't use the hard board. Mine is just indoor/outdoor carpeting cut to fit. The head rests keep it in place on the front and the seat latch and other protrusions keep the carpet in place on the back. I usually put his bed on top of that for longer trips. My behind the seat cubbies are always full so he can lean back against the stuff (tool bags, windshield washer fluid bottle, etc). The good thing about the way I did it, I can roll the carpet back and it stores behind the seat so I can have my full back seat in a matter of seconds, and no plywood to store. Your write-up gave me the inspiration though!