I was about to throw the Dremel down on the table and stalk off in a state of medium dudgeon (not quite as extreme as high dudgeon, but headed in that direction) when I saw the handle of the foam brush and had that proverbial light bulb flash over my head. I spent the next 43 minutes trying to find my errant necklace, finally discovering it wedged into the pages of a tech manual on the computer desk across the room, then had to find the right size of handle to fit the internal diameter of the tube without a) splitting it down one side, or b) being so loose it didn't hold firmly enough.
A few minutes of trial and error, and finally hitting on the idea of padding the handle with strips from my hubby's roll of shop towels, I had a working solution! In addition, my polishing time jumped up exponentially faster, mostly because I wasn't having to chase the slippery little buggers down every two minutes. It had taken me almost 45 minutes to polish one of them, and took me an hour and a half to polish the other 13. Woohoo!
So, in my little world, things are looking up because necessity is the mother of really strange inventions, like shop towels on a brush handle to stabilize and hold a tube of silver so I don't fry my fingers or break another window, or scare my cats, yet again.