Charlie, If you can, use a wool mop, dripping wet with the Free all after you are done with the last match. Put a rag with rubber band over the muzzle. Let that Free All sit for 4 hours to a couple of days, then brush. You will notice a big difference in how the carbon comes out.
Last year, a friend passed and my brother bought Billy's Rem 7400 in 30/06. This 7400 had never been cleaned and the muzzle's bore looked as if it was gold coated. I put a cork in the muzzle and filled the barrel completely full of Free All. 8 Months later, I pulled the cork, and a blueish slurry poured out of the bore. The Free All had gone down beneath the layers of carbon and Copper and had free'd up the fouling, but some still remains. I need to brush it now.