My year-old male Persian was having similar problems with urinating in a couple of different spots outside his litter box. I took him in to the vet, who ran a bunch of tests, and it turns out my cat is diabetic. The diabetes was causing some kind of a chain reaction in his system that contributed to sediment and a UTI. I'm going to have to put him on a special diet. Right now, he's on antibiotics to deal with the infection, and I'm hoping his habits will return to normal.
Good luck with your cat.
Good luck with your cat.