The only history they can trace - if they can trace any at all - would be to the shipper and maybe the jobber or other dealer house.
Beyond that, the trail would grow cold.
Doesn't hold out a lot of hope for all those modern-day fans of TV's CSI being able to tell in a matter of moments, does it?
No 'trace evidence', no blood spatter or fingerprints, no hair and fiber evidence, no attitudinal-personal-agenda-driven-wild-assed-but-right guesses from lab rats - no nuthin'...
Men have dropped, rested, lost or otherwise completely forgotten their weapons since they figured out weapons - civilians are the worst of them, but hunters are no slouches, either, and soldiers routinely leave their piece leaning while they get chow, while cops put their shotguns on top of their vehicles and drive off all too alarmingly often.
The point is - while interesting to be sure, would this be 'as' interesting had this been a Hopkins and Allen or a Crescent shotgun, or is it interesting 'only' because it's a 'Winchester - the Gun That Won the West' (though one article quotes Houze as saying it was Remington - go figure), and 'everybody' knows that Winchester was the only lever-action rifle filling scabbards and fighting off Indians and Outlaws during the days of the Wild, Wild West?
Headstamps aren't going to help, by the way - ammunition wasn't expended back then like it is today during a 'Shoot-Fast' meet, and a lot of it stayed on the store shelves for decades - just as it sat on shelves in Line Camps and Bunkhouses, so older stuff would still be around and available for quite a long time.
Unless it's poorly stored, ammunition lasts a helluva long time - even blackpowder-loaded ammunition, with the old primers will still surprise you every once in awhile if it was kept in a dry area. (In Vietnam, we routinely drew .50 Caliber Machinegun ammunition that was brand-new in 1943, and every round fired, because it had been properly stored and kept canned-up.)
As to NCOWS - they allow far more different firearms than SASS - they just don't allow all the modifications and modern stuff - to them, 'modern stuff' means 'Colt New Service'.
Vaya,
Scouts Out!