I got the longest I could find, because of my side drillers. I was surprised to read that longer, not taller, was the fix. Go figure.
To answer your question, since Miss Kitty isn't a side-driller, I think the size you are looking at is just fine!
The Home Depot in my area, still carriers Sterilite boxes. They may have taller ones, that don't have the "dip" in the bottom. I assume you are looking for a box with tall sizes, due to the "digging to China."