Oh i have that problem too, infact its worse because our litter box has to be in the lounge, our laundry is our entrance and way to small, and there is no where else, i have a small house, ive got a better litter now and i dont get the dust i used to, it was terrible, i think your invention is just what i need. give my girl some privacy too.
I notice sometimes lexie does a pee and does not cover it or dig, do your cats do that, the other she always digs and covers, and sometimes for pee too, must depend how she feels on the day eh