It's been a long process. Moby has always had moments of peeing outside the box. Even when they are kept perfectly clean. We have always assumed it was an artifact of his early experiences before we found him. Bathtub peeing is pretty normal for cats. And Moby has always loved a throw rug on the floor. A few months ago, he started to use the carpet right near the door, probably because the door into the bathroom, and the litter boxes, was closed, and he didn't feel like bothering to scratch at it for me to open it for him. The presence of dogs, and possibly another cat, along this hallway, may have caused him to want to mark. No way to know for sure. But a trial for us, and a lot of cleaning up and vigilance. Moved his food nearer to where he was going, which contracted the area that smelled like a perfectly good alternative, now.
Three things seem to have finally solved the issue. First was the deodorizer that denatures the urine, really kills the smell, although it has a strong smell of it's own. We ordered a pad that he can pee on, easily washed, impervious backing. He took to it right away. And I finally remembered how much Moby loves the smell of Indian food. He doesn't eat it, but he will sniff in obvious pleasure when we have it around. One place, our neighbors always cooked, the most lovely of Indian food aromas would fill the hall, and he would sit where he could get the best wafts. So, I thought, maybe Masala spice sprinkled, would give his brain a different message about the entryway. Sure enough, he has not gone in that area, or anyplace outside the bathroom, since.
We can live with this. Old guys just get peculiar about where they take a piss. Has to be expected.