Just curious if it's only cast bullets that cause the ring.
No, carbon deposits build up from propellants regardless of bullet composition.
+1 on this and one of the favorites to help with this is the "Double Tuff" brush from Brownells. If you use the Dewey rod or Handles, and like to swap with an adapter the "special Line" brush is strong and fits right on a Dewey Rod.
Just go with a Larger caliber for the "cylinder Only " chore. Eliminator (by Bore Tech) is a good for this also. And it does not smell with strong odor, like some others.