Put heavy motor oil on and around the surface where you see rust, then dip 4-0 Steel Wool into the motor oil, and Gently-- I MEAN GENTLY-- Like you would if you were rubbing your own BUTT!--- burnish the flowers of rust of the surfaces. Flush the rust out of the wool regularly, as the rust itself is ABRASIVE!
Done right, you will be left with tiny little pits in the barrel. You can touch up the metal with browning or bluing solutions as the case may be. I recommend heating the barrel up with a torch, after cleaning the surface with alcohol to remove all oils, hot enough for water to sizzle before applying cold blue or brown. It opens the pores, and those HOLES, to let more blue or brown solution contact the metal. Do this a couple of times with the barrel hot.
Now, flush the barrel with soap and water, and go over the area with baking soda and water to kill any acids remaining. Dry, and wipe down with alcohol to get off oils from your own hands. Then heat the barrel up again, and this time, spray it with oil. The oil will burn and smoke- stay UP wind of of the fumes, and don't breathe them. Let the barrel sit and cool to room temp overnite bathed in the oil. The Oil will deepen the color and work down into those pores, to make sure there is NO MORE bare metal exposed to the air and moisture.
Oil or lube the metal for normal storage, and shooting. :thumbsup: