Soaking is your friend.
If bore solvents don't do it fast enough, use a gun safe carbon remover.

The worst carbon problem I ever had was the gas cylinder and muzzle brake on my AK-74.
I tried everything........ packing them with paper towel and soaking with bore solvent, using a lead away cloth, and Slip 2000 Carbon Killer, nothing worked.

Then just as an experiment I used Shooter's Choice Extra Copper solvent and the paper towel packing.
To my surprise the carbon was removed down to the hard chrome plating.