I have a large Thumbler Vibratory cleaner. You say you tumble wet with pins. Do you have a drain in the tub? I think this might be a possibility. I really don't like the dust. I think it would be good to eliminate it.
I pour off most of the liquid, then dump the brass and pins into a RCBS media separator. After a bunch of cranks, the stainless pins and lots of water fall out and the brass stays in the cage. I pour off the liquid from the pins, rinse several times, then pour the damp pins back into the tumbler. With the lid off, my pins are dry after a couple days here.
I then take the top off the cage, put the lower half with the brass in a big water filled tub and rinse multiple times. I then run the brass through the media separator again to get most of the water off. I then lay the brass out over a large bath towel. By the following day, they are all dry, clean, and shiny.