Removing modern markings is done often on replica CW muskets for those who want an authentic look. It's called "defarbing." (I have no idea where that term comes from!) On replica muskets, the Italian mfg markings, BP only warnings, etc are removed from the visible portion of the barrel.
In your situation, you only need to remove the markings on the visible flats. Why waste your shop time on flats covered by the stock? Be sure to remove the markings at full depth as some will leave a trace impression even after the visible portion is removed. You might not see this until browning or bluing.