Cool! Sounds like you and Zig are making great progress.Perch trained, petting and eating with you right there... Way to go you 2!
Cleaning cage bottom? Depends..is the grate removable?
At any rate a stiff brush or plastic scrungie thingy to get poops off and wipe down with apple cider vinegar and water. If removable you can clean it in the tub
And even if he doesn't like bathes yet, still offer it..maybe he'll decide to take a dip. I use a plastic sandwich container,tried numerous tubs and dishes before Levi decided he like the sandwich thing. WITH a piece of lettuce LOL
Ziggy hasn't attempted a tub bath yet..but he does like a nice wet piece of lettuce clipped to the side of the cage and bathes that way