We had a cat like that. Majik, spayed female, would pee on everything she could, but would use the litter box only if it was the last thing around. We eventually tried putting a towel in her box (each cat had their own box), and she finally started using it. If it was messed up or burried, it would have to be switched so that she would use it, but at least it was easier than washing quilts every day
My parents still have her. She was mine, I got her as an early Christmas gift in '97. She hates my other cat, Bo (bottle baby), so I had to let her stay with my parents. But she is doing good, and they now have 2 new cats, my grandfathers 19 year old girl and a 4 month old kitten that I bottle raised.
Don't know if the towel thing might help, but you never know