As far as your dogs getting into a covered litter box, my cats were adults when I got my dog, so we just put a gate up to the room that their litter box and food is. They can jump it, and the dog cannot.
I could probably have installed a kitty door into the door of the room that the cats could fit and the dog couldn't. The dog is bigger, but he is not enough bigger that he wouldn't have given it a good try at fitting in the door, though.
I 'think' my vet told me I could sprinkle meat tenderizer on the cat's food, and the dog would not be interested in their poo anymore??