I just got this from a very reliable source. You’ve nailed the reasoning behind “Box” and “Chest” numbers. The DCM, NRA, and shooters were concerned about variations in accuracy between the beginning and end of large lots, such as the 1935 Lot 1846 which consisted of nearly 3 million rounds. The answer was to break it down into smaller quantities or sub-lots, such as the 1500 round “Box”. That way, a shooter could be issued ammunition that he could reasonably assume was consistent. Or at least more consistent. Whether it actually worked out we have no way of knowing although it probably gave a shooter more confidence in his ammuntion, and you should never underestimate confidence as a factor in winning or losing.
But, as I said before, once out of the box, the ID of the ammunition lot number is lost, unless you had a list of Box numbers cross-referenced by lot number. And, it doesn’t explain why some cartons were marked with the lot number and others weren’t. And, it doesn’t reconcile things such as the 1930 Match where over 3 million rounds were manufactured and yet all cartons were labeled with the lot number. But maybe the “Box” thing was something that evolved over a period of years.
Do you suppose shooters back then fought over who got ammo from Box 1156 because it was so much better than Box 1292? There’s no doubt in my military mind whatsoever.