That's the thing - no way to know exactly what happened with these rifles. Your story is interesting but I doubt the "N" is Navy.

The "script" P was used by both RIA and SA - RIA until the end of production in 1919 and Springfield until somewhere in the 1913-1915 date range. The stock with the small "S" on the foretip is definitely Springfield. Of course, after the rifle left the Rock Island Armory, hard to tell where it went or what happened to it.