A 20ga shotgun brass brush is just about the perfect size. Attach it to a short cleaning rod, or one segment of a larger one, and chuck the other end into an electric drill. Use the lowest setting, drench it in your choice cleaning product, and back it in and out of the chamber several times. That'll pretty much clean it out thoroughly.
Another issue could be a burr in the chamber...even old rifles with lots of use can throw a burr sometimes. Check your cases for scratches after extraction.