I didn't have a bit of problem with the pillow case and I didn't even use the plastic stuff on it. The HP dries any manure that gets on it and it's easily displaced after that. While it's still wet manure, I just tossed some bedding on top of it so the chicks wouldn't get in it. Easily done when checking water and feed levels and takes less than 2 seconds to do. At the end, I just remove the pillow case, shake it out and wash it.
My chicks would perch on that top during the day, but always slept for the night down under, so not much poop on top of my HP brooder at all. The way to accomplish that is to turn down the HP accordingly so it's not too hot for them to sleep the night underneath the brooder. That accomplishes two things...they actually go underneath it at night for warmth because the top of the brooder isn't warm enough for nighttime sleeping and the poop they deposit all night is now in the bedding instead of on top of the brooder. By the time they are sleeping on the brooder at night, it's time to take it out of the brooder altogether. No need for plastic one can wipe and such if a person doesn't want it.