Cheerio said "thank you, JAZZO"
First of all - my three kitties including Cheerio live exclusively indoors.
A feral cat has never had first hand contact with humans and is therefore weary of us, and of course, it lives outdoors. A cat is considered feral once it has spent more than 12 weeks without human contact. The more time they spend that way the more difficult it is to tame, provided that one can capture it.
I feed a pretty large feral colony. Most of those cats don't come even ten feet close to me, some come closer. There are different degrees but the bottom line is that you cannot pet them.
Along the way I have TNR (Trap Neutered Returned) more than 80 % of these feral cats. I have found permanent homes for more than 20 kittens that I have tamed, bottle fed and cared for until they were ready to be adopted.
Cheerio herself is half feral. I have trapped her when she was close to 20 weeks old. It was somehow easy to tame her because she was sick so she didn't ahve enough strength to fight me. She is now only coming to me but when I get her she will stay calm for somebody else to pet her..although trying to escape.
Actually all three of my kitties come from the same place. Frosty I have nursed since he was 11 oz and Tippy, I think she has been abandonned there and possibly been traumatised becase she has been friendly but has a hard time living indoors. I have to constantly work with her to work on her shyness.
I am relieved that you don't have to deal with an UTI.
Have you read Dr. Jean's "LitterBox Secrets" parts 1,2,3, and 4?
I now that it doesn't bother you if Sampson does his buisness in the bath tub but it might be a better way to fix the problem. I hope those articles can give you some clues.
I know you have the patience so perhaps in time, taking small steps you can find a way.
Here is the link to the library. You can scroll down from there to "Litterbox Secrets". There are so many small details that may not make sense to us, but make a whole world of a difference to our kitties.
Let me know if I can be of any more help