Any of you not have a rooster but are willing to try one? A neat experiment would be to see if rooster can get hens to lay eggs in boxes you use. My adult roosters clearly effect nesting and thus egg deposition sites for my hens that are in pens and free-ranging.
My roosters like to do that, too. They get in there and make a big fuss and play house while the harem stands around watching. I think they are especially helpful with pullets that are just about to lay. It's so sweet. But they can be clumsy with the eggs.