OK, with much trepidation, I got this thing apart. The lens has some foggy/scratched places on the outside where it was rubbed with a dirty, dry cloth... or something.

I'm thinking of polishing the outside only (because the inside looks good and I don't want to re-do the lettering) with a headlight polishing kit, starting with the finest grit polish (which would be the thhird and final step if I were polishing headlights). Any other recommendations for polishing it?