Rig the brake up in a drill press at very low speed and spin it against a piece of ultra-fine sandpaper.
My Redneck Brother!
Reading along before I suggested the same.
If you are gonna redneck something, ya gotta be redneck smart.
Back that paper with something dead flat.
OP. Are you similar with figure 8 sanding.
Not my choice, but if you proceed with your idea, at least YouTube this method.