I made it. I took cardboard and laid out a template for where the platform should rest, then cut a piece of plywood for the platform as well as the forward support piece. The armrests of the seats are an ideal support just a bit lower than the seat back when folded. I simply put a hinge on the forward bottom section to attach another piece of plywood for support, then took it to my local auto upholstery guy to put the carpet and velcro on it.
In time the velcro was not real effective in 'sticking' to the factory carpet on the backs of the folded seats, so my iteration has been to add two more features:
a) a simple latch that holds the support piece more or less at 90 degrees, and
b) use bungee cords underneath attaching small eyes I screwed into the bottom side of the platform to nearby fixed floor pieces like the base of the seat. This way any inertia from a stop with the weight of the dog won't allow the platform to move around.