If it's not UTI and neutering didn't fix it, there are some other options to try. Some cats don't like clay litter very much. You can try the newspaper like one or the little pellets type. Or you can shred some rags and stick that in his box since he seems to be attacted to peeing on soft things (very common for cats that have litter box issues, the newspaper litter may help too since it's softer). Also, put hte litter box in areas he likes. The closet is a good place since he's known to go in there, and it's hidden. Some cats don't go to the bathroom in the litterbox if it's out in the open, they feel vulnerable. You can also get another box, the more boxes there are the longer they stay clean, and a cat may not use a dirty litterbox. Also make sure there's a box on each floor of the house, if you have multiple floors. I had a cat with this problem once, but no matter what we tried it didn't fix it. He had been a stray for 2+ years before we adopted him (he was 2 when he showed up at my BF's work, starving and cold). He just couldn't adjust to being indoors, and having 5 other cats in the house didn't help. We ended up taking him to a shelter, hopefully someone adopted him he was a really sweet cat despite his issues