As far as I have found, there is no chemical out there that can clean the carbon out and not destroy anything else.
I soak the comp with Shooters Choice to loosen the carbon. If the build up is real bad, I'll use an engine turning brush on a dremel to get it out. You have to be real careful around the crown.
From then on, spray the comp with Dillon case lube after every stage. This keeps the carbon loose. When you clean the gun, use Shooters Choice and a cotton swab and most of the carbon will come out. For any that is left, I use a piece of a Scotch brite pad soaked in solvent. Lock the pad in the end of a pair of hemostats and clean out the ports.