I think you probably don't want to use steel wool on aluminum. Use the green scotchbrite pads, or fine aluminum wool if you can find any.
I got a buffing pad that goes on my electric drill and used black buffing compound, followed by brown, followed by white and it shines like chrome. Stays that way a while, too. At least three months in the weather without signs of corrosion coming back.
Chris in Boston
Oh yeah- for the actual chrome, I use the cotton-y stuff in the can, pull out a wad and wipe. Smells like there a petroleum product in it. You don't even rub, only wipe and then wipe off the residue in a little while. The rust comes off, the corrosion comes off. Works great.