Ha, got me there Coach!
I've started using that stretcher slot for hauling things, so that extra piece of foam now goes "behind the couch" between the folded up bed and the ambo wall. I can also store it below the bench, in the long compartment there. In pic#3, those two pieces of plywood hinge up and access one big compartment. You could move the first set of hinges out more, and change the other panel sizes, to make a bigger storage spot for thicker foam.
The other two pieces of foam form the couch back and seat cushion.
For now it's all held in place by the barely-tightened ratchet strap. Ideally I'd have some kind of latch mounted on the wall that secures both ends of the couch back so it can't hinge forward/unfold. Then the foam would be upholstered and held in place to the plywood with velcro or snaps. I've thought about adding some trim on the short ends of the couch back to strengthen up the plywood, and prevent the strap from compressing the foam.
No problems so far with the foam compressing. I think it's a seat cushion foam, it's rather firm. We got a foam mattress topper pad that makes it a lot more comfortable. Foam came with the van. PO had made a version 1.0 of this setup, with just two pieces of foam, but it wasn't well thought out, so I re-did it to hinge like this and have 3 pieces so you could have the seat, back, and filler piece.