After the hot soapy water bath, I then take my barrel outside and pour about a coffee pot full of hot boiling water down the muzzle of the barrel, letting it run out the nipple and bolster clean out hole. Then get a glove or towel and grab the barrel and bring it back to where you are cleaning it.
This is ALL I do to clean a bore-it has workled perfectly for me for over 40 years of BP/ML shooting. I use Birchwood-Casey Sheath after the bore is dry. I have totally given up on all commercial solvents. Water is all that is needed to clean a ML of all BP fouling!