I wasn't thinking of making the final article from foamcore - far too bulky. Mat or greyboard seem the right sort of stuff.
As it happens I prototyped one this afternoon out of corrugated cardboard, just to see how it could work, and it really will be eminently possible with the right materials. I found a few ways of doing it, some more wasteful of materials but "tidier", others more fiddly but less wasteful.
Trying to make a "folding bottom" (as in a commercial film holder) seemed far too much bother. One solution is to forget about doing so, and instead simply leave the bottom of the film slot "open", but with a couple of layers of velvet ribbon as light traps. Good enough perhaps for paper (if one takes care), rather less sure about film. The bottom end of the darkslide slot can made sealed of course.
It also occurred to me that this would be an excellent project for some clever dude/dudette with a 3D printer ...