By belly, I mean the belly portion of the hide. See how the brim of my hat is a little wavy? It kind of potato chips and curls on me. I think if I had stayed in the upper part of the hide, it wouldn't do that. If I run into a piece of stainless wire that will take a bend, I might do a binding around the edge with the wire inserted.
As to cleaning, I wouldn't have a clue. Leather n' Rich is marketed as a leather cleaner, which I use it for on things. The hat, I just hit with some antiquing gel, some saddle tan dye and the Leather 'N Rich a couple days later.