The USS North Carolina online archives shows a rifle in their collection listed below. Unfortunately, this photo detail did not list the destroyer it came from but maybe the curator has more info.

"M1903 Springfield rifle, ca. 1903. Serial number: 1137808. Engraved ”US Springfield Armory / Model 1903 / 1137808.” Ordnance stamp on wood stock. Stock stamped ”FJA” and ”AAR” and D? 13 and (square with dot in center) R (triangle). Two stamped small number 18 in circles. U.S. issue leather sling with brass attachment pieces. The rifle and bayonet were removed from a nearby destroyer during BB-55’s prep for mothball. Bolt has been removed for safekeeping.
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