Oooo! That's a nice rifle. You should be justly proud.
I have little doubt that the rifle is a USMC rifle and it was taken out of service before 1939. So, it matches the story that goes with it.
In answer to your question, Yes, there are USMC rifles all around your rifle's serial number. And it's not coincidence. From my data base:
S/N 1009309, S.A./11-42 bbl
S/N 1009338, S.A./8-42 bbl
S/N 1009445, S.A./11-18 bbl - your rifle
S/N 1009818, S.A./7-18 bbl
J.B.