I don't have Alcoa's but I have alloy wheels and they were in terrible condition. My Sidekick was from the OR coast and someone tried to remove the oxidation and clearcoat with sandpaper and screwed them up, following the removal of the oxidation he spray painted the wheels and that turned yellowish.
I decided to refinish the wheels and bought a couple of cans of clearcoat remover from Pep Boys. I used my 7" sander/buffer from HF and a set of cotton wheels and their polishing and buffing compounds to get a great shine. Some of the sandpaper marks were so deep I used 500 and then 1500 W&D sandpaper to remove the marks. The smoother the finish before buffing the easier it will be to get a great shine.
I bought a can of spray paint for the area between the spokes and when I get back from Idaho at the end of the month I will finish the job by clearcoating the wheels. My local bodyshop(I've known the owner since High School) suggested the remover and clearcoat. I'm getting a quart from a auto paint store and will use my gravity sprayer.
The remover is very hard on you if you inhale the fumes. I used my 3M Dual Element Mask I use for sanding and painting. Some places took two or three application of the remover and a nylon scrub brush.
It's a lot of work but those wheels really look great.
PS: smacdiesel is right about keeping the shine but it is nothing compared to keeping Brass, Gunmetal and copper polished in a submarine.