Forgotten Weapons made a video on three M1903 "snipers" in the upcoming James D. Julia auctions. Who wants to see it himself, visit
https://www.youtube.com/watch?v=-dWICTS0g-E
What was interesting to me (aside the funny screw heads on all scope bases) was the leather scope can one rifle comes with. I captured a few screenshots, which fit into the discussion here - see attachment.
If I'm reading the serial of #645.991 correctly (please correct if someone has a different suggestion), it's not SRS listed, but right within a block of USMC rifles, and right next to a handful of SRS listed snipers in the 646.xxx serial range.