Disney considered the litter box to be an all you can eat buffet - gross! Anyway, the way we stopped her from "snacking" was to use a covered litter box, turn it into a corner so she couldn't get into it but the cats could by jumping and put a 10 pound weight on the top of the lid (otherwise she could pull it off).

I have all my litter boxes in a room in the garage that the cats have access to through a cat door but when I brought R&R home they were too small to go through the cat door so I had to have a box in the house until they were bigger.