1) Corrosion X to eliminate, or naval gelly (ph acid) to stop corrossion. Clean and Oil.
Don't use a Rust Converter because it forms a film of "converted rust" that is 'paintable'. You don't want that coating.
2) You might try Ospho or similar phosphorus acid ( concrete etcher at Lowes is usually phosphoric acid). ex: http://www.wmbarr.com/product.aspx?catid=103&prodid=221
When you treat steel or cast iron before you paint it, you can use phosphoric acid by wiping wet pads or brush on the phosphoric acid - it eliminates any rust - leaving a light paintable phosphoric coating
depending on the product, you then rinse (in water, ironically) the acid off and quickly blot dry it to prevent flash rust. This might eliminate any light coating (whitish) of the ph acid, but then OIL it immediately.
In the case of your barrel, you could dap a wet rag of phosphoric acid in the immediate area of the rust, wipe off (it will leave a phosphoric 'coat' to protect the metal), and then oil the crap out of it to prevent any flash rust.
I'd test under the barrel (against the stock) to see if you get discoloration, if so you may want to take the barrel off and do the whole thing for uniform color, or rinse all the ph acid off and use a hair dryer to dry immediately after the rinse. Use nitrile gloves so you don't get acid on you, and don't get oil/salts on your rinsed barrel.
It doesn't sound like you have a big problem, you could just dab back and forth some ph acid in the rusting area and then wipe off with water towel, then immediately oil.
my 2 cents.