Thanks for the replies! I doubt it's a medical issue because this has taken place over 2+ months and it's always the same couch, not all over the house.
Yes, enzymatic cleaner. I ran out of Nature's Miracle and we're snowed in until tomorrow, so I used Pure Ayre. Good idea to really saturate it. Unfortunately we can't limit his access to that room unless we lock him in the basement, which would have other ramifications. I put a little bowl of food on the couch based on the concept that he won't pee where he eats.
I have a couple moody teenagers, so the moody cat is fitting right in. Calgon, take me away!