A quick and dirty way to make foam core more rigid is to coat it with fiberglass - Home depot or any autoshop should sell glass mat and resin - or you can find it online. Make sure to get epoxy resin, as the polyurethane stuff eats away foam core - it would be good to reinforce corners and load bearing places.
I though of doing this as well, but I was considering making big box with a smaller sliding box in front that held the lens, that way I had some limited focusing distance. So with a 24" lens, I was going to make a big 24" cube that had a smaller 18" or so cube in the center the opposite face of the film plane that slid out to 36". I wouldn't rely on my calculations, but when I tried to figure it out, with a 24" lens this gave me focus from 5 feet to infinity.
I have abandoned the idea for now, since I decided I really wanted movements and 1:1 magnification, so I'm trying to figure out bellows.