The only thing I have found to really clean the inside of cases is SS media. I would be more concerned with that. I wipe them down between targets during a match. Some powders and loads leave a lot of residue inside the case. That is why I would want them clean inside to start a match.
I thought I was getting my .223 and 6mm brass clean using a wet SS process with a cheap Harbor Freight tumbler. It was nice looking, I thought. Yesterday I took delivery of a Frankford Tumbler. Wow, what a difference.
Before, with the H.F. unit, I could see slight stains inside the primer pockets after 90 minutes, but after using the Frankford for the same 90 minute session, the brass is absolutely new looking. Plus there is less damage to the case mouths, perhaps because the Frankford drum is so much larger and holds so much more water. I had been filling my H.F. drum only 60% full of water to keep it from weighing too much. With the Frankford I essentially fill it up. I should have bought a Frankford in the first place.
By the way, since I moly coat my bullets, I don't worry about ultra clean case necks or the need to individually lube the cases prior to seating. I let the moly do the job of lubricating the bullet/neck interface and I have noticed a reduction in ES and SD.