Sounds to me like your rabbit is spending a lot of time sitting in that sheltered area, and also sitting on whatever type of food dish you are using. Most rabbits tend to poop and pee where they sit; a lot of does will do this in their nest boxes if you leave them in the cages with them. Most people advise building cages with all-wire floors for this reason.
Clearly, your rabbit prefers not to sit on the wire. He may have sore hocks, or he may just prefer the solid surface. My answer to this would be to put a wire floor in the solid area, and put a sitting board on it. He will still be pooping in there, but the board can be easily lifted out for cleaning. I would also change his feeder to a hanging type that he can't sit in.
. I moved some out side in the open are but he didn't like that. He also he pops in his food. I had rabbits before and had one trained to use the litter box.
