Just switch over to stainless steel pins in a Lemshine or similar cleaning bath.
Your cases aren't as shiney or polished looking, but they're clean and the inside fouling is removed as well.
Just a quick rinse with hot water (so they dry faster) and you're finished.
You can use your original tumbler, which takes almost as long, or you can get a rotary tumbler, like those used by rock hounds.
The stainless pins are re usable and last forever.
I bought a five pound bag appx 15 years ago, when I was first informed about this on CGN. What's left will last a lifetime.
Lemshine is cheap and the whole process is much less messy/time consuming.