MGM is exactly right! You shouldn't do anything to that rifle!
I love '03's and have two Remingtons, and '03 and a '03A3. Actually I've also got an A1, but that's what my 338/06 is built on. And no, I didn't! I bought the action already butch... uh, "sporterized!
In your case, if that rifle is 90% except for some pitting in the end of the barrel, you ain't got a problem! Leave it alone!
I remember when K-Mart had racks of 03A3's for sale for $49.95!
Ah, those were the days!
A few things you say interest me academically.
This gun was built in 1944 and has all the correct markings. It was arsenal rebuilt after the war.
What makes you think it was rebuilt after the war?
I am going to try shooting it and see how well it shoots. If it shoots any sort of reasonable group, I will leave it alone.
Don't expect a sub-MOA rifle. I believe 4 MOA at 100 yds. was all the military required. They normally do shoot better though. I've shot HP (Match Rifle since you can't shoot them in Service Rifle anymore) with mine.
If not, I will probable set it aside as a collectors item and put it up for sale.
And "leave it alone." Right?
I am told that this is a very rare model in fairly exceptional condition
In what respect? I think '43 and '44 were the major production years. I believe Remington acquired the tooling from RIA in '41, began production of '03's in early '42 as I remember, and the rifle morphed thru what some people call the '03M into the 03A3. Don't quote me on the dates as my memory comes and goes nowadays and I don't feel like taking the time to look up the exact dates.
Anyway, I can't think of a variant that would make it a "very rare model." Maybe an A3 marked A4... kinda doubt it though; who knows...
The alternative would be to purchase a new 1903 barrel and have it installed.
I doubt if you would gain anything! by doing this.
Just my 2 cents. FWIW