Try this:

Start in walnut to clean - add cut up used dryer sheets to soak up the dirt. It really does make a difference.

Follow with the superfine nut media from grainger (sp). It's like sand and geta every little nook and cranny but never gets stuck in the cases.

A guy at my club turned me onto it and it's fantastic. I add a little Nu Finish to make them shine.

Here's a link Nut-Based Media, Random, 5 Lbs. - Tumbler Media - Tumblers and Media - 5UKA8 : Grainger Industrial Supply