Have you considered simply using aluminum foil and Coke? That's what I use to clean all my rusty chrome. It is 100% safe, cheap, and available at every grocery store in the world. Wad up the foil, pour Coke on the part and on the foil and start scrubbing.
My understanding is the tiny amount of phosphoric acid in the Coke reacts chemically with the aluminum and rust to melt it away. Also, you can scrub the heck out of chrome with aluminum without fear of scratching the chrome ever. Chrome and steel are much harder than aluminum.
Vinegar is stronger than you think. It will make any pits in your chrome deeper. I left a hammer head in vinegar over night once to try to clean it up and the outer 1/8 inch of steel had turned to mush by morning. Seriously strong.