Scota4570,
I generally follow Daryl's shooting program with my rifles, but considering your problem, try the below....
Not sure why the crud ring has started forming, but try this for a remedy - the English method for target shooting. Fire the rifle, then pour the powder in the barrel, follow with a over powder wad or your best facsimile. Swab the bore with a damp patch, then load patch and ball. The grime gets forced onto the wad and does not contaminate your powder or touch hole, yet allows you to clean the bore.
You can make wads from milk cartons etc if you don't have any in your rifle caliber. Try it and let us know your results.
Curtis