We have been using storage bins their about 12 in. deep, no cover. Even with our big boys things stay in the box most of the time. The only problem we have is Little Bear and Bart. Bart has steam shovels for paws and I've seen litter go 3 feet in the air (big hand fulls). Little Bear likes too dig for China and makes sure that the litter does not fall back into the hole; she can shoot it almost 5 feet. Bart goes for altitude and LB goes for horizontal shots.
We only use 4 boxes for the 12. 3 are the bins and one is low (3 in) for LB and Lucky only. I did put plastic walls on 3 sides of LB's box, about 16 in high. This way with she with her bad leg and Lucky still a kitten they can get in and out, but the litter can only fly in one direction.
Any time we have tried covers we find more around the house than in the boxes.