Thanks guys. I think I'll pass on the Coke approach. Seems you could do the same thing with Windex or anything else and a scrubbing pad.
I've had good luck using 4 and 5 aught steel wool pads for polishing in the past, but the plating is unusually thin in this case and either the base metal or application process are lacking. I think any real effort would simply rub the chrome off, not unlike those cheapy plastic radio panel bezels some manufacturers used.
Probably the best approach is to experiment a bit with a couple pieces using vinegar, or baking soda and water, or ammonia etc until I find something that works. Fortunately I do know enough not to make chlorine gas in the kitchen sink.