Re: droppings
If you want to retain the nutrients in the droppings, they need to have a good carbon:nitrogen ratio and be protected from rain until incorporated into the compost. I know you've not had rain for a while, but when it comes....
The book Salad Bar Beef (get it from the library) will explain the logistics better. It would be in the chapter where he explains the bedding pack he uses in winter.
Ahh, so I need to have my compost pile sheltered? I can do that. It's conveniently on a mounded area which should keep the rain from rising up to the heap. I bet I could make a simple tarp roof for it.
For that matter, I could scoop up the whole thing into the coop where it'll be more protected without needing to make anything new. I think you and @mariannewest were saying that's the better route to take.
I know the new poo will help a lot, but is it not beneficial to have a bin outside the coop as well that can have things in it that the chickens would eat? Or is the carbon/nitrogen of the leaves and chicken manure enough?