I have polished a bit of aluminum and second everything said here, particularly Caswell. Very nice people, was a father and son team but I think it has expanded. If the piece has large flats, go for the stitched wheel on a good buffing machine. Watch your grip and your hands, wear heavy gloves.
Here is the best hint I can give to anyone living in "Industrial" America. Industry is dying, so look in the Yellow Pages for "metal finishing, polishing". Most of these are small "job shops". Things are universally slow, they will talk to you about jobs they would have laughed off 2 or 4 years ago. The guy who did the aluminum trim on my '64 Plymouth last year told me that in 1999 he had over 400 competitors in New England, now it is below thirty. (hearsay)