The advice in your last picture is spot on. I have had success with #0000 steel wool and metal polish in particular.
Advice for polishing and cleaning up nickel plating
via Erik Bruchez https://www.facebook.com/groups/705152958470148/posts/1230905545894884/
Others recommend penetrating oil or WD-40 in combination with 0000 steel wool which should be enough to remove corrosion, but not damage the nickel plating.
I've also seen Marty Morren suggest 0000 inside Dremel tools for dealing with nickel plated key rings.