I haven't messed around with the jewel, but...
You could probably use some metal polishing compound instead of sandpaper. It's basically equivalent to a really fine sandpaper, but the surface would not be scratched. I have some "Genie" metal polishing compound, and it works on much more than just metal.
Another thing you may want to try is a real fine steel wool; this should not scratch the surface as much as sandpaper.
I'm not sure if any solvents will harm or even work on removing the green, but you could always test a small amount in an inconspicuous place.
I'm curious about this, so post back if you give any of these a try.