I know this is an old thread, but I just stumbled onto it, and since I have Remington 1903 A3, I wanted to be able to find this thread again. Thanks to this link, http://m1903.com/
I determined the rifle was made in 1943, and even found a photo of one, which I saved. I removed the military stock long ago, and have no idea what happened to it, and the photo was a good reminder of what it looked like. Clearly stamped on the barrel is “RBLT. August 25, 1945".