I can think of a few solutions. You could decrease the size of the opening in a couple ways. You could decrease the height of the opening by adding lumber across the top especially, but possibly a little at the bottom, too. The chickens could still hop over it and a smaller opening will allow less poop in. You could also maybe halve the size of each opening by putting a piece of plywood or something similar to form a wall, cutting the opening in half width-ways. The chickens would probably like that, tucking themselves in behind a wall, stepping in and then stepping behind the wall to lay. Another idea would be to create some smaller boxes, ones with a least one closed side to face out and a lid, and put them within those larger spaces but not facing out. The chicken steps into the nesting space, then steps into the smaller box to lay. That should be appealing to them, too, but there's always the possibility that they would just lay in the remainder of the larger space.
It's a struggle to figure out what will work best. I've remade mine a dozen times in a couple years. I just tried again recently, only to put everything back the way I had it before.
