Thanks, you guys. I fear the polarization is a film layered onto the lens exterior and would probably suffer for the polishing. I don't need prescription glasses so the shades are just to protect my sun/wind sensitive eyes. Brasso wadding is available here--I've used it for years--but not as easy to find as liquid Brasso. Any USMC boot would know where to find it.
I have used jeweler's rouge previously but that was on real glass with the polarization not applied as a film. My current shades are Ray Ban, cost $150, and are considered to be cheap! The $200+ shades I've bought I lose in the first week.
I think I'm gonna' try a small amount of Brasso in a corner of the lens.