Rock tumbler / barrel polisher
A strange concept for a polymer workshop but these are used for lots of things other than rock tumbling.
The basic concept is that you add some sort of abrasive media to the barrel, a little liquid, and then chuck your items in, and the rolling motion of the barrel sooner or later either sands or polishes whatever you put in there.
Many jewellers use them to clean and polish precious metals using a funny mixture of stainless steel balls and pins called "shot".
I use mine a lot for tumbling silver, but have yet to findi the best media / medium to add to the barrel to sand or polish polymer. I've tried green ceramic cones, hard white cubes, rocks, small rocks, tiny rocks, rounded river rocks, sand and sandpaper. You can also try adding barreling liquid, fairy liquid, and pumice powder to the water.
I'm sure something will work but, perhaps because it's fairly light in comparison to the media it's surrounded by, polymer seems to take days and days of tumbling before any change in its surface becomes apparent. I'm a bit too impatient for that. Still, I will continue experimenting (anything that makes sanding and polishing a bit less of a chore!).
Let me know if you find something that really works - it could be a great step forward!