ED, I feel your pain! I'm very experienced with the model A, I have rebuilt many (new balls, etc.) They brake 'friction' surface wore quickly and there wasn't a remedy supplied by ND. New brake shoes added some life but they aren't available any longer. I have heard of some guys having 'flame sprayed' a new brake surface inside the big end of the hub.
Back to your question, no, everything in the diagram is needed but another nut isn't needed if the parts are assembled and tightened properly. Mind you, this isn't a good brake but for careful riding it works fine. I added a modern day 'caliper' brake to the front wheel on mine and I use the Model A only for forward motion.
If you have all the pieces shown in the attached diagram you have what you need. This is one of those situation where I say: "I wish I had that wheel here and I bet I could fix it!"