I think the rust occurs BECAUSE iron particles have been exposed, else there wouldn't be any rust, right? Isn't the whole idea of a stainless steel that a chrome oxide of some sort forms over the surface and sorta covers up any carbon or iron particles?
So, if rust forms, it means that something has removed the chrome oxide and uncovered the iron, yes?
So I think you have to get the iron GONE and then allow the chrome to oxidize again to prevent further rust.

I'd vote for a try with the Barkeeper's friend, using the oxalic acid to eat the iron. As said previously, try in on an out of sight area.

I have tried citric acid on stainless steel that I have hot forged. when hot forging stainless steel, two problems occur since we are seriously disturbing the chrome oxide coating:
-iron particles come become exposed (and they rust later)
-carbon particle become exposed (and they stay black forever)
While the citric acid may have some effect on both issues, it is miserably slow in my limited experience. The oxalic acid that I use for cleaning erector set girders works slowly too, but a lot faster than does citric acid.

Pete Stanaitis
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