I don't love to do anything that takes time and patience. Plenty of time - no patience. The only reason I mentioned time is that it's always involved with patience.

Try polishing with a Black and Decker "Mouse" sander (vibratory), a piece of felt and your favorite polishing media. Finish with some automotive 'glazing' compound. I found those ceramic cooktop cleaning pads to be excellent along with some polishing compound. They look dangerously like a Scotch pad but are 100 times less aggressive.