Quick update. I tried three different methods just as a little experiment: WD-40 and 400 grit, blue Roloc, and maroon Scotch Brite. I was deliberately non-aggressive, just wanted to see what a little effort would produce.
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Below is Scotch Brite
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Next is Roloc
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And finally the sandpaper
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So, I think I'll hit the entire thing with a Roloc wheel and finish with Scotch Brite to see what I get. The areas where the rust stains are, look a lot worse in the photo. I can barely feel them with my finger and can't catch a fingernail on them at all.