As promised, I am reporting back on my spinning composter. After 4 weeks I had compost. Some of the leaves that got stuck on the spikes inside the barrel didn't break down. They stayed in the barrel for the second round.
After the first day of use, I immediately realized that I needed to improve the design just a bit. I ended up putting duct tape on the outside of the barrel to keep the nails in place.
I also discovered that some handles would really have helped with the spinning of the barrel. Before I added the second batch of yard waste, I added some old kitchen cabinet knobs that I found in my basement.