Add some thermal shooting and you will really give them the what for! I have drastically cut down my population with the ratinator, jiffy mix, poison(where the chickens don't go) and my nightly battle maneuvers with the thermal and a suppressed 22. Keep it up!! Sounds like you are getting it done.
Lots of good ideas here but stopping feeding the rats doesn't work. They can find food anywhere and they won't leave a good shelter, especially with winter coming. We had rats living in our barn years before we ever had chickens, and there was no animal food out there for them to eat back then. One even lived under our house in a groundhog burrow once! Weirdly, that was just one rat.Or you could stop feeding the rats and they would leave.
Really, it is that simple.