Thank you for your help, gentlemen!
Attached is a pic of my ~20+ year old Midway 'tumbler'. I suppose it's more accurately a vibrator. When I first got it, instructions were minimal. I filled it, dropped my cases in, and turned it on. It sort of vibrated, but even after leaving it run overnight, the cases were still dirty. By accident, I screwed the lid down tight while it was running, and lo & behold, a vortex action began!!! Media from all sides began flowing into the center, and down. I could see my cases bobbing up & down in the flow!!! Fantastic!!!
So it cleans the cases quite well, but doesn't really leave a matte finish. And it doesn't touch tarnish. So I guess the 2nd case in my pic is as good as it'll get.
I might try the crushed corn cob on another batch tonight, just for comparison.