Stop in for a cup of coffee

How about light rubbing compound?
The best polishes ARE compounds. Not sure if paint compound would be more or less aggressive. The trick to getting scratches is it needs to cut, but not make more scratches and dull it. I tried 'turtle wax' brand that I have and it did not seem to do much. Used same pad on a drill with mothers and pad turned black, so I know it is cutting.