OK, our cardboard testing has uncovered that:
1) Our cats will avoid a litter box that has a high entry point, even if there’s a stool leading to it.
2) They’ll deal with stepping over an 8” high wall.
3) An 8” high wall is enough to keep most of the litter from getting onto the rest of the bathroom floor.
Also I read in Indoor Cat that cats do not like doing their business in closed spaces, but I don’t know how much to trust that book.
So, the new design for the litter box cabinet has a low wall and is partly open. This is going to be like $70 of plywood, which makes me wish they’d just make a small Litter Robot that could fit in that nook.