I was right were you are 6 months ago. I had such hugh amounts of dropping, I had to use a shopvac to get all of it out. Here's what we did:
1. I bought a baffle ( lid) for my feeders that hang with a chain- No more varmints dropping inside or chickens pooping inside.Ordered from Fleming outdoors-less than $4.00 each.
2. Mixed plaster of Paris with peanut butter made a paste, added a little veggie oil, rolled into balls and set on top of my metal feed can in a pie tin, leave out a tray of water, the water allows the PoP to harden quicker inside the varmint. The plaster of Paris will kill the mice over time, but their bodies will not be toxic to what ever eats the dead rodents. I'm careful to keep it high up and behind a locked barn door also 25 feet from said door. I have dogs also. I only put it out as needed, no droppings then I don't put any out. Took a month to start seeing bodies last time, usually you don't see bodies because they don't typical leave the nest when feeling ill. However, I did see a a hugh drop in the amount of dropping I was seeing early on.
3. Rewired the coop with small diameter hardware cloth. Wire over any holes or 1/4 or larger cracks. Flexible skulls these mice and rats have, they can restart their heart too.
4. Making sure I have no feed spills that aren't quickly swept up. Removed all feed at night into a closed and locked barrel. removing any veggie or treats before night from coop and/or run.
Try these tips and let me know how it goes.