If I recall, my screens fit perfectly into a 5 gallon bucket. (I just don't use them that way.) Anyway, it wouldn't be hard to make a receiver, or base, to bolt onto the top of a vibratory tumbler that would hold a cut down bucket. When time to change batches/buckets, you just lift off your bucket and set on the next one. The bucket would contain most of the dust, and the motor on those vibratory tumblers is sealed I believe. Even if not, the motor would be fairly divorced from the works.
A bit more work, but you can also remove the tumbler jar from the vibratory tumbler fairly easily. This would provide a nice flat base to work with.
That could work I believe, and be relatively safe. Just keep any dust that got loose cleaned up, which we always need to do in any case.
Yep, my screens do fit into a five gallon bucket, and of course, are stackable too: https://www.amazon.com/gp/product/B0...?ie=UTF8&psc=1
Vettepilot