Go with the recommendation of the manufacturer.

I have seen polishing rouge at Sear's.....available separately or a 4-pack (different colors). Use that cotton wheel on a fairly powerful tool, because it is doing a lot of work when done right. I have polished aluminum fuel tanks for my karts using a massive pedestal mounted grinder motor. Polishing is polishing......not sure what "deep cleaning" means.
Show us the pics when you're done!!