I want to add on to this thread since I have a similar question, just a different braking system.
I just overhauled my coaster brake the other day, cleaned it out, degreased the bearings, and the regreased them with Phil Wood grease. When I took the hub apart originally there was some really waxy type grease or material in there, all over it. I didnt go crazy with the grease I put back in there, just the bearings and the threads that activate the brakes. Should there be liberal amounts of grease in this thing or is just doing the bearings what is proper?
It just seems like it doesnt stop smoothly and it went back together correctly.