I basically use your method.

After the poly gloss coats, I will sand up to 1500 g or 2000 g wet and dry paper. (or scotchbrite pads)

Then I use a cutting compound, polishing compound and then Maguire's Scratch X applied using a small (and quite cheap) random orbital polisher from a car care store. (The polisher is only good for the front and back, not for tight spaces)

Someone on the forum recently had success with a compressed air polisher!