Somethings to think about:

What would be the explanation for the USA-F markings appearing on shotguns made in 1939 - at least two years before war was declared (December 1941), three years (1942) before the first purchases were made from Hunter Arms Company stock, and three years (1942) before receipt of the first orders from the US Army? If the US Army was planning on these purchases as early as 1939, why did the Hunter Arms Company have to scramble to complete the first order (1941) by filling in with Ideal Grades and odd configurations?

Secondly, what would be the reason for the position of the hyphen between "Armed" and "Forces"? Separating Armed Forces with a hyphen would be unconventional. Has anyone seen a hyphen used between those words?

I believe that the explanation is a lot less interesting and less complex - simply a barrel inspector's mark. After all, the Rochester Ordnance marks were much more prominent and placed on the frame. Why mark the barrels? In addition, the location of the barrel mark is in the same as others that one occasionally sees. For example, I have a Specialty with JJ stamped in that location.