I'm not a great fan of covered boxes. They seem to generate many more problems than they solve.
A lot of cats have that problem. Well, you know, all four feet are in the box, how are they supposed to know their fannies aren't!
My favorite solution is to get a big rubbermaid storage bin, 14 gallons or larger. They're tall, and big enough for large cats. The high sides prevent the hanging-over-the-edge thing! The one I have is like 33-gallons. Nobody misses with that!

The plastic used by Rubbermaid is sturdy, odorless and easy to clean. They do have ridges on the bottom but they're rounded and not too difficult to work around to scoop.
Cheers,
Dr. Jean