Black Talon,
I've used Iosso (case cleaner) with real good results in the past, but cheaper yet, and reportedly with great results, many guys have been using a couple of capfull's of mineral spirits in their tumblers.
I tried Mother's Mag Wheel polish in the past and it worked great, but that black residue really makes a mess out of the media.
Ammonia is the big killer for brass, and if you find a good liquid brass cleaner that is devoid of it, it should work just fine in the tumbler.
I've used 3M Imperial Handglaze on cars in the past, and although it's about $30.00 a bottle at NAPA, I've tried it on brass by hand with a rag. It worked exceptionally well, and I think it'd work great in a tumbler also.
Like it was mentioned here, walnut media is really non-absorbent, and adding liquids might not work as well. A cream cleaner, or rubbing compound, that dries down to a fine abrasive (1500-2000 grit) probably would be a better choice to work with the walnut media.
Hope this helps....
Bob