I haven't tried this, but I have notes that tell me you can use a solution that is made with 3 parts ammonia to one part water for ultrasonic cleaning. It is used to clean some high tension parts in a scanning electron microscope.
I did the aluminum foil and baking soda the other day to a couple of really nasty looking silver coins. It pulled the tarnish right off with not work at all. Plus it doesn't remove any of the silver, the electrochemical process actually turns the tarnish (silver oxide OR something like that) back to silver. So you don't get any metal loss, like you would with polish.