Jason: I use a formed patch around a stab jag, one that has been pushed thru the bore several times to "squeeze" it down, then coat it with JB, worked into the patch with the finger. Run it thru the bore one or two times. If I'm real careful, there will not be any JB deposited on the face of the breech.
Then use a snug fitting bronze brush with a bore guide, and give it 10 push strokes, from chamber to muzzle. Yes, the brush is removed after it exits the muzzle. I never pull it back across the crown. Then one dry patch, followed by a patch wet with Hoppe's. Let it soak for a few minutes, 3 or 4 dry patch's, & 'scope with the Hawkeye.
Depending on how much carbon I see, I may or may not repeat the process. As said, I do not attempt to take it all out. I just want to keep it under control. If I took all trace of fouling out, the barrel would then require 10 to as many as 20 fouling shots before it started to shoot again, a waste of ammo & barrel life.
Most of my barrels are Krieger & Bartleins & they are all cleaned with the same routine, usually about every 300 ( with varget powder) to 400 (with VihtaVouri) rounds.
Recently broke in a new 6BR, 8 twist Krieger and had a section of copper buildup in the grooves only, for a distance of about 6", midway down the barrel. I tried Butch's with o'night soaking, Sweet's & Warthog 1134 with the 10 to 15 minute time limits & none would remove the copper, as verified with the borescope. Patch's coming out white do not indicate a clean bore! I have no idea why these solvents, especially the Warthog, (previously worked fine) would not remove the copper, but 10 push strokes with the JB & bronze brush removed it all.
I know some will dis-agree with the above, and so be it. It works for me and all verified with the borescope.