The plywood is (labeled) 19/32" sheathing. I had a sheet of it in my little pile of plywood. It seems to be just fine as is, for me. I'm not very heavy though. I have something else I'm going to try too, and then pick which is better. That piece of plywood is very "splintery" and if I use it I'm going to have to glue on some light carpeting or something, just to spare the cushion from snags and rips. If I had a power sander, I suppose I could make it better by sanding it.
Re the floor space, I think I could have made the box even narrower. I made it 32", but 30" with a 2" overhang with the top cantilevered out would have worked too. Or 31" with a 1" overhang, whatever. Moreover, when I stuck the dinette cushions on there and laid them flat, they hung out 3 or 4 inches into space and still were functional that way. Probably because you don't actually put any weight on the outer 3 or 4 inches of a mattress, but it still supports your arms. So I could have built a 28" box and still used a 32" cushion, I think. That extra floor space would be good for smaller dogs, shoes, etc.
Good thinking on the pics. I'm a very linear thinker and often cannot see simple ways around an obstacle.
:/
That's why I'm a prolific poster in the forum, because I get a lot of good ideas, many of which are obvious to someone not thinking like me.
:)