This is probably not a very valuable reply, but back in the day when aluminum hard hats were OK to wear in the oil industry we used to shine them up by dipping them in a vat of caustic soda that was kept around to clean tools with. A few seconds in the vat and the hat came out plenty shiny. Not sure that this method would be commercially available anymore, but caustic soda should still be around. Maybe the chemical stip places like Metal Rehab as 6Cyliners suggests above would have something similar?
