All good advice but I'll add one thing: if you've done everything that was suggested and the problem still continues, you might want to talk to your vet about medication. All of my cats are rescues and a couple of the boys had a pee war going on for a while. After doing all the things that you did, tearing up carpet, scrubbing floors, etc., I'd had enough. They were checked out, it wasn't physical so that means it was behavioral. My vet suggested a med called Clomicalm. It started out as a med for dogs w/aggression or separation anxiety issues but it's now routinely given to cats for behavioral issues. I give them 5 mg. at bed time. (You can't miss a dose or they may relapse.) Since then no side effects, no problems whatsoever and the pee problem is history. They've been on it for several years and I have blood work done yearly just to be safe.

I know you probably don't want to resort to medication; I didn't either but the alternatives that you mentioned just weren't viable for me either. Try all the other options first and if they work, great, but if they don't, Clomicalm has saved my house and best of all, it saved my cats from being secluded in the basement. I would never rehome them for the very reasons that you mentioned. Good luck and keep us posted. And btw, welcome to Pet Talk!