I had the same issue with the chickens sitting on the feeder, solved it by buying one of those metal galvanized shallow pans which was about 4 inchs wider than the base of the feeder.
I cut two slots about a 1/4 inch wide, 1 ince long each side were the handle goes into the feeder which allows just enough room to snap one side off when I need to fill it. The galvanized pan is upside down over the op of the feeder which then it over hangs the base were they eat out of; the galvanized pan is about 20 inches wide and 4 inchs deep.
The hens still roost on it but the droppings don't get into the feeder, keeps the rodents out and as a side effect when it really rains hard or storms it keeps the feed dry.