At one time the Ordnance department issued a slip-on pad that did not require alteration to the rifle. I think that after WWII some company made a duplicate of this. I do onot know if they are still available.
Cmon guys- shoot one of those "S" stocked M1903 through a 100 shot regional match with hot handloads or the old M1ammo and cloth 10-X shooting coat with no shooting mat. That would make a "flincher" out of a cigar store Indian.