Don't use a dremel. If you want the stock to look even all over wrap a piece of sandpaper around a deepwell socket that will just fit inside the barrel channel and sand. As the channel opens up, move up to a larger size socket. This won't take any longer and will give a professional look. If you order a stock made for a varmit barrel you probably want need to do this. If you order a sporter stock then you will.
All of my go-to guns have aftermarket syntetics, 6 McMillans, 2 Brown Precisions, 1 B&C, and 1 High-Tech Specialties. None of my rifles shot any more accurately after replacing the stock. I'm not spending $600 on a stock for a gun unless the gun proves it is already a tack driver. If it won't shoot, it goes on down the road. If it does then it gets a better stock. Not to improve accuracy, but to reduce weight, get a better fit, and to just plain look better. B&C does not make a lightweight stock, they are all heavy, but for this use that is not a disadvantage. My only B&C stock is on my FN Patrol rifle. While heavier than any other stock I own, it is almost 1.5 lbs lighter than the Hogue that came on the FN.
I wouldn't recommend a B&C for a hunting rifle, but on this gun it is just as good as a McMillan or HS-Precision costing much more. If your current stock is the Hogue, it is a big step up in ergonomics, but I doubt you will see an increase in accuracy.