I think you'd have a lot more people responding if they could see a picture of the fireplace to give you better help and advice. I think this is really a creative idea. I can't wait to see pictures of it when you start work!
I agree with whoever said to lay down vinyl flooring in the bottom of this coop. Make sure you have a lip on the bottom so that your litter isn't scratched or flung out, either. So I'd have a deep pan in the bottom. You could even build a "removable pan" in the bottom of the coop. It could be a deep litter pan that you pull out and dump and then fill back up again with pine shavings. When the pan is removed, you could vacuum the inside bottom for any shavings that fall out.