I use some stuff called Harvey's rust remover. It comes in a powered form. I paid like $2 for it. I put it on a damp sponge and it wiped right off. I couldn't believe it worked so easy. The sponge starts to get hot it must have some kind of strong reaction with the rust. Best stuff I have ever seen. I used CLR but had to scrub and scrub and it still didn't take it all off. I bought this stuff and it worked like a dream. I bought it at Menard's. I am not sure how big that chain is. It is like a Home Depot/Lowes but on a lower scale. I hope you can find this stuff. Here is the manufacturer.
William H. Harvey Company
Omaha, NE 68117
Sorry no phone number, Good Luck