What's the best way to remove a light coating of rust from a carbon steel paella pan? I was recently given a carbon steel paella pan with a very light coating of rust (its prior owner hadn't known how to care for carbon steel, and gave it to me and bought a stainless one).  There are quite a number of ways to remove rust, and I'm wondering which one will work the best?


I have a jar of Naval Jelly, which I use to remove rust from garden tools.  However, carbon steel knife forums warn that Naval Jelly can be too strong and etch the carbon steel.
A vinegar bath is another method (as well as other acid baths such as citric acid).  However, the paella pan is 15" in diameter, and I don't have a large enough basin to soak it in, nor am I eager to buy 3 gallons of vinegar.
Some people simply scrub off the rust with steel wool.  I'm concerned that this will scratch up the paella pan, which is otherwise fairly pristine.
Brasso is milder than Naval Jelly, so I was thinking of just using a tube of that.  It's not, however, primarily a rust remover.
It's possible that scrubbing with Barkeeper's Friend would take the rust off as well.  But it's also possible it won't.


Recommendations?
I would start with Barkeeper's Friend. That has worked for me in the past.  Use it with a synthetic scrub pad.  As you know, once you get it in shape to use it, after cleaning, a light coating of oil wiped on with a paper towel will keep the rust from reappearing during storage.