You have to polish steel, so you'll need a long, small polishing wheel to get inside the barrel with a polishing compound. The dremmel has small polishing bit that can do it, you just need some kind of extender to get it down the insert.
You can buy the polishing wheel by itself, then put it on a drill of some type if you want to go budget.
Another option is finding someone to polish it for you.
However, I think it would be cheaper overall to just buy a new insert if you're not emotionally attached.