I used a cloth wheel(s) from harbor freight on a battery drill with green rouge, followed by a wheel with white rouge, followed by a wheel with Mother's Aluminum wheel cleaner.
But first i used a 2" wire wheel on the drill to remove the oxidation, then sanded with a random orbital with 80 grit followed by 120, 220, 400, 1000, 1500, 3000 before starting with cloth polishing wheels. You can get it just about as shiny without all the sanding, but the surface isn't flat and doesn't look as mirror-like.