Thanks very much, PPs! We saw the vet yesterday, and through we're still waiting on urinalysis results, the vet is 95% sure it's behavioral, not medical. Glad my cat isn't sick, but ugh!! Vet recommended something like the litter you mentioned, PP, and adding a litter box. But we're also going to put the cat on Prozac. Better living through chemistry, even for cats.

. Seriously, I think it will be good for him. He's gotten increasingly needy over the years, and this may calm him some.
If that doesn't seem to solve the problem, I would definitely consider a behavioralist! I'm not willing to rehome our cat, but this situation cannot continue as is.