I just spent about an hour going over the G5 with Bar Keeper's Friend and I got it back to a nice satin luster. It isn't exactly mirror-like, but it's very smooth to the touch. The machine has only one really bad 'battle scar' to one side of the headlight lens. I'm probably going to keep working on it periodically, but I'm happy with the progress so far. I finished it off with a coat of car wax, just to help retard further oxidation. And for good measuret, I even put some Armor All on the plastics, It definitely looks better than it did.
Here are a few photos of it after a round of Bar Keeper's Friend:
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