I guess that's one advantage of having a large coop. My "poop board" is the floor. I refresh the litter in most of the coop on a regular basis during the winter, but under the roost I don't bother.
There is plenty of room below the roost for 3-4 months accumulation. That's why I have a semi-annual schedule of cleaning and disinfecting the coop. The manure from the coop only goes to the compost pile when I'm able to turn it in. I can take a current picture (January) of it, if nobody's sensibilities will be offended.
As for kitchen wastes attracting vermin...yeah. We always bury fresh refuse when we add it to the pile. If the compost pile is frozen, or covered with snow (like mine is now), we used a dedicated garbage can with a secure lid. In my case here, it has to be dog-proof and bear-proof. I use rubber garbage cans because I found even the galvanized ones will rust out.