I'm aware that some cats may dislike certain types of litter. *But that's
not the problem -- He goes inside the box when I keep him in the utility
room. *He did his duty in the box for about 2 days while in the utility
room, I cleaned the carpets, let him out, came home, and there was poop
in the living room. *I even put a second litter box in the garage, and he
didn't even make an attempt to use it.

IMO, I would add another box in the living room, near where he has
gone recently. I realize that this may not be an ideal place for a
litter box, but it's worth a try to see if it solves the problem (and
it sure beats cleaning the carpets). I would also add another low-
sided box. It's possible he finds it difficult to get in and out of
the box due to arthritis or joint pain.