My method for polishing these up involves more the use of sandpaper. I start with 220 to get the deeper scratches out, then go through the different sandpapers all the way up to 3000 grit. It is easier if you don't skip any, so what I have been able to find is 220, 320 400, 500 600, 800, 1000, 1200, 1500, and 2000, then 3000. It gets easier as you go. To go from 3000 to polishing with a wheel is a snap. Without the bench polisher you can't get the super shine, it is simply a matter of RPM.
This sandpaper isn't free, though, but what is your time worth?
I keep the sandpaper in a big tupperware bucket with a little dishwasher soap. you might be able to do three whole machines with each piece! Autobody shops sell this stuff.