I'd try using less litter. I know you say they like to dig to China, but that doesn't necessarily mean that they wouldn't use it if it had less litter. We switched Josie from a huge covered litter box that held 40 pounds of litter, down to a LitterMaid that holds 2 inches of litter. Big difference but once we put them together, she only used the LitterMaid. You might have to change the litter more often, but it might be worth not having it all over the floor.