Forgive my ignorance, but.... Why do you think that crabs on the doors won't get flipped into a box trap the same way they will on a topless one? The only difference is the top. Do they bounce off the top when the door flips them?
They do flip in the boxes occasionally, I run a 1:2 ratio box/topless, I mark my floats so I know which is which, and occasionally pul a box as fast as I pull topless, that's when I'll see a flipper, sometimes a mumbo will flip 1/2 way and come up with little resistance. Guaranteed to put a smile on yer face when ya see a mumbo when ya thought ya were just gonna check the bait.