There are automotive carbon cutting solvents you might consider. But, 150 yrs ago in the reserves, we were issued a rotary cutter that would twist onto the threads of the front barrel bushing. Spin the crank handle, a cutter would turn and chip off the carbon - symetrically. Keep adjusting the cutter with a screwdriver (?) and all the carbon would be gone. I doubt you'll find one for sale anywhere. They were probably hand made in some military workshop. But it is an idea.