The problem with a blued gun is, the bluing is not all that durable.
In removing the carbon, you usually wind up doing more damage to the blue than if you just clean enough to prevent build-up from causing the cylinder to rub on the rear of the barrel.
You CAN remove most of the carbon, but the bluing is going to take a beating, and you'll wear it down to bare metal fairly fast.
The best, least harmful method I ever found was to use a brass "toothbrush" and powder solvent to scrub the cylinder face.
ANY polish, no matter HOW fine will quickly remove the bluing.
Even fine polishes like Flitz are STILL abrasive and will wear the bluing off.