I am completely against putting animals down, and would never do it myself.

That said, I agree that spending his last days locked in a laundry room, no matter how many cozy blankets he has, is no way to live. I'm sure that he wants to be with you and he's probably completely embarrassed about his incontinence (most cats would be). If your only two options are putting him down or locking him away, putting him down seems more humane to me.