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Tomato juice, vinegar, orange juice, or lemon juice could be used (ph range ~ 4-2).
Or you could probably use chrome polish which usually has an acid in it, but I'd test a hidden area first... the combination might be a tad aggressive, causing a dull spot.

I've used brass wool occasionally on neglected parts.

The Mohs scale kinda explains why aluminum doesn't scratch the chrome.
Aluminum's hardness number on the scale is ~2.5.
Iron is 4, but rust is probably weaker.
Chromium is 8.5.
Diamond is 10.

Which got me to wondering if there is something else out there that would be good to use instead of the aluminum. The only thing that comes to mind is gold leaf, but that would be a tad expensive.

Warning, should exercise caution during this procedure.