Sounds like you're not using a progressive press? If you were, you could simply run the brass normally...through the deprime/sizing die--and the media would be removed by the deprimer pin.
Another alternative is: stop tumbling. Ultrasonic produces far cleaner cases and clean primer pockets (in my experience)...but I don't do either any more and am not likely to clean brass ever again. But, I shoot handgun and you may be talking rifle. I think my entire reloading process became about 1000% cleaner when I stopped tumbling--no rouge and no dust and no garbage everywhere. Just water everywhere.
I simply don't clean my brass much anymore--it's a complete waste of time as near as I can tell. Off the floor, into the press. Done. Haven't done it in quite a while and haven't noticed one tiny bit of difference in anything at all, except I save a lot of pointless fuss.
The loaded ammo looks about as clean as the cleaned brass reloads to my eye. I'm not handloading precision bench rest rifle stuff--so naturally that makes a difference in your perspective.
“If I had to live my life again, I'd make the same mistakes, only sooner.” T Bankhead