You don't actually want a "polish" as in shiny in your chamber. You want a fine crosshatch not unlike an engine cylinder-- a nice matte finish. A mirror polished chamber is one that is more likely to gall and stick. Especially if you're shooting a stainless barrel. The crosshatch will hold a tiny bit of carbon and help ensure you get smooth case release.
I solved a chamber issue using a Flex Hone brush and it made me a huge fan of the product. It just works. My chamber was so bad that not only was there extraction issues but the brass was coming out with a stippled pattern on it and it was contributing to stuck cases.
A flex hone for the chamber solved all this. I bought the .243 brush because it would be small enough for 308, 7-08, 6.5cm etc and not do anything to the neck really. I don't think they offer one for the BR family of cases, but you can get a diameter close enough to what you want because you are really just targeting the body area of the chamber and not neck or shoulder.
The flex hones cut slowly enough that you can easily control the degree of honing (especially with the 800grit I bought) so you won't have to worry about going too far.
12mm size is .0472" and should work perfectly for massaging the body area of the chamber. Get an aluminum oxide abrasive in 600gr or 800gr and you'll have this solved easily.
Do you need a cylinder hone for your small diameter applications? Order your Flex Hone tool from Brush Research today.
www.brushresearch.com