Armed with the suggestions here, I ordered a bottle of the California polish over the weekend and looked forward to its arrival, especially with the possibility of going to Oshkosh and the need to get the entire plane looking halfway decent.
When I got home yesterday evening, it has arrived, so when my wife went to bed, I headed to the hangar ("this polishing thing is a real sickness," she said. Accurately) to try it out on a small area.
I wasn't that impressed. I found it APPARENTLY much more abrasive than, say, NuVite's Grade S, which is the final step. While it provides *a* shine on the aluminum (and there already was one on the metal I was polishing, just not the total mirror, no swirl one I'm going for), it didn't seem to provide THE shine.
I'm going to try it a little bit more.