Boy.......that is a sweet one and from my standpoint it sure looks totally righteous! Looks like the R stamps are all in the right spots, front sight hood you have (usually missing), type 8 stock.
Pics below are of my 03-A3 sold several years ago, and according to markings and Joe Poyers book (4th Edition) was all correct. Mine was February 1943, and was an estate purchase with an original sling, Military M-1907, Marked G&K 1918, further marked W.T.& B. Co. So the sling was a 1918 by Graton & Knight, leather by Westboro Trunk & Bag Co.
Further research showed that the US government in early 1943 was in such a bind for arms for the troops that unissued stock from government stores was sent to Remington for immediate issue to the troops. The brass fittings on the sling had been chemically blackened by G&K before government storage.
The sling I have is basically still "unissued" in that the leather is very supple, no cracks.
Funny thing.........when I listed the 03A3 for sale, the sling was attached, but when a Buyer came around and made a full price offer, he did not want the sling at all! He was not a collector, just a 30-06 hunter/shooter and wanted another one for his kid, cause he had two, one for himself, and the wife.
So..........it sits in the holster/sling stash.
I'm not into 03-A3's anymore so if you are interested...PM me.