Ok that is bigger than I thought, so glad you were able to answer that. So give deep litter a go and see how it does, you can make adjustments if needed.
You really don't have space to do poop boards so scrap that. Is it possible to put both roosts at same height so the birds spread out a bit more? Yes folks do use sand as a substrate in coops, though I have no experience with it.
Deep litter may help with your mud issue but it looks like a...