Aatay, Craig, Dennis, Terry -- thanks!
I think I can now articulate the problem. Based on the link above from Kraig, it appears that the 3-prong brake disc should be attached to the clutch by a snap ring (mine is loose, the 3 prongs are not attached or lined-up in the corresponding slots on the clutch). In my ignorance, I thought that the break shoe should push the 3-prong break disc against the clutch and and it would magically find it's way into the slots while rotating by a push from the break shoe. Now I am thinking that the 3-prong break disc should always be lined-up with the clutch slots (and held in place with a snap ring) and the "smooth" side of the break disc is engaged through friction with the shoe.
In summary, it seems that I need to find a snap ring and somehow position the 3-prong brake disc against the slots in the clutch. Does this make sense, or should I provide a Rosetta stone for further interpretation?