I tried some of the
Lyman Tufnut which is walnut media treated with rouge. I didn't like it since it left residue on the inside of the case that didn't want to come off. It does shine the brass nicely.
I use plain media with NuFinish like you have, and I just run the tumbler until the brass. It doesn't take much electricity and I like the protective finish it leaves on the brass.
I have seen several posts mention adding some Comet cleaner to your media to improve the cleaning action. I'm not sure I want that much abrasion when tumbling.