Here is a slightly different approach that works well for me on light rust "freckles". Wet barrels down with liberal coat of transmission fluid. Let sit a few hours and wet again. Then use a new single edge razor blade to gently shave rust spots flat. Use short strokes. Keep spot you are working on wet. If blade loses its pritine edge, switch to new blade. End result looks good, feels smooth, but must thereafter be kept clean & lubed to keep any rust below surface from "re-activating".

A Springer Spaniel, a 6# double and a fair day to hunt.