But seriously, you can use those hanging feeders and all, that helps. What kind of feeder are you using currently?
I use the 12 lb hanging feeders and when the chicks are grown I put them inside a black rubber fortex tub to catch the beaked out food (not hanging).
When they are very very tiny, I just use an open pan inside the brooder. They do poop in there some, but I don't like the traditional chick feeders with the little holes. I have had chicks get stuck in them.
I prefer the troughs with the spinners on top, but even those are not foolproof. On the other hand, I wouldn't lose sleep over it. Chickens have been pooping in their food for millenia with no problems.
Keeping your feeders and waterers raised as high as possible helps a bit though, especially when they get to big to perch on the edge of a range feeder.