Grid Bottom Cage for Guinea Pigs?

I know that guinea pigs can develop sores and injuries by using gridded bottom cages. Unfortunately i didn't know that when i bought my cage, so i've come up with possible solutions that might work (you tell me lol). If i put towels or fleece over the grid would it be piggy safe? Also, could my pigs' feet get injured if I leave a little section of the grid showing where i hang my hay rack so the extra hay can fall down?