Barrels from another gun fitted to this one at Remington......

RJ3 is a Remington repair code for December 1940. R = December J = 1940. Looks like the boys at Ilion took the barrels from another gun and renumbered them and fitted them to the gun in question.

Dave is correct. Ilion inspection stamps all over them.
The mystery is in the two sets of repair codes.

The factory letter that the OP refers to was dated December of 1940.

Seems like he has his answer right there in the Remington codes stamped on the barrel flats.

Maybe I'm just dense but maybe the 'factory letter' might tell us? What does it say?

Parker letter as rquested
 

Great info coming in. Intersted if anyone can confirm member Ronig comment on OV being factory code for Trojan steel. See letter from factory below regarding barrels as requested.

OV is the grade code for the Trojan Grade gun. Can you post a picture of the breech face of the barrels. The Trojan gun does not have a dolls head extension and none of your pictures shows an extension. Do your barrels have a doll's head extension?

Bill,
Yes the barrels gave a dolls head. I'll post a photo later today.
Thanks for the info.
Dan

It would have been a simple matter for the factory, be it Meriden or Illion, to replace the Trojan's rib extension with the proper (for the gun) rib extension with doll's head.

Left side of lug looks to be stamped "D grade for 2 3/4" shells." If so marked that would be correct for Remington made Parker barrels. Looks conclusive that Remington used barrels on hand to fit a set to this gun.
The letter is a nice piece of provenance for this gun.
Erick