Hey Lewis! It has been many years since I was on my Springfield kick so I may be somewhat off here... But as I remember, if the receiver ring is marked Remington 1903 it was one of that company's first production rifles in late '41 or early '42.
Remington had bought (?) the old Rock Island Arsenal tooling and received a foreign (Australia?) contract for 1903 rifles. They are fine receivers...
Since your rifle has been sporterised I imagine the barrel has been cut down. The barrel ID marks (year and ordinance stamp) are located behind the front sight so are probably gone. If it is the original barrel they were also a good-uns but from your description who knows.
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No biggie...
Just check the bedding, crown and headspace, shoot it and see what you get. It should shoot as well as any used sporter you pick up.
Years ago I bought a sporterised Springfield 1903 in the A-1 serial number range (just about the only difference in the high numbered 03's and the A-1 was the move to the pistol grip stock). It shot 150 gr. bullets very well!
I had the late Dick Nickle rebore and rechamber it and it is now my beloved 338-06!