I had the same problem when I got a kitten from the shelter. He would pee in our bed in the middle of the night usually on my side or me! It didn't start right away I don't think but we just kept putting him out on the screened lanai at night for a while. I keep the litter out there but when he first came I had one in the bathroom so that wasn't the cause. Thank goodness he doesn't do that anymore. But if he can't go out he has now decided that my oriental rug is the next best choice. Fortunately that is rare!

I have 2 litters also but one is covered & they ( I have 2) poop in that one but seldom pee in it.

Hope yours gets over it.
PS: I washed my down comforter & put it in the dryer & it was fine. It was a light weight though. I doubt if I'd try it with my new heavier one but who know's.