all i can say is its a real pita, doing it with the "right kit" I am in the painfully slow proses of doing the better part of a 55g that i got cheep as heck. I have read for on the cheep side of things swrill remover works well (for auto paint) on the light stuff
For really cheap you could try brasso. It s brass polish, lots of people use it to remove scratches out of cds. You can get it all walmart or the cleaner section at your local grocery store. I've used it successfully to remove scratches out of cellphone screens before with good results. Use a fabric wheel on a fast corded drill.
For faster results, you can use a blue all purpose buffing compound first and finish with the brasso. The buffing compound I'm talking about is the stuff that comes in a block and looks like wax.
i've been using these pads as algae scrubbers on an acrylic tank. the tank had some deep "mag-float scratches" so i started with the 4000 grit. you couldn't even see the sanding with water in the tank. i've since moved up to the 6000 grit. the kit i have goes up to 12000 grit for the final polish.
it's been a slow process, but it's easier than moving the tank!