Are you working on the clear coat over color or the color coat?
Making the finish flat and polishing should be two separate functions.
Brushing on a nitro lacquer finish will not help, spraying is a better choice.
To get it flat I would start with a random orbit sander and a good quality no clog paper like 3M free cut gold maybe 120 grit.
put on a coat, sand it and take down the high spots and repeat until it is perfectly flat.
then start going up to the progressive finer grits.
If you want a satin finish the lines that 600 grit makes will do it reasonably well but you need to go in straight lines relative to the case parts.
If you want high gloss I would continue with random orbit sander until about 1000 or even 1200 and then go to rubbing out with rubbing and polishing compounds.
You need a rigid backing on your sander if you want to get the finish flat thats why I suggest random orbit. It also helps to have a vacuum attachment for your sander to help reduce build up of dust nubs.
Another option try to sell your current air hockey and manage to buy a new one, at least you may check here
if it seems more acceptable for you!