Given enough money, and enough time, you will find what you are looking for. I do not recommend taking an original military rifle with a good barrel and replacing the barrel with a criterion barrel. There will be a loss in collector's value and it will cost an additional $300 to $400 for the new barrel.
I did build up a M1903A3 from a stripped receiver and installed a criterion barrel. The criterion barrel was superior to any military barrel I have had on any 03 or A3. Military barrels were either worn, or wartime barrels that were not that accurate.
Sometimes you have to build a rifle from parts. I had the Remington receiver, and it took years to find all Remington parts, (with the exception I wanted a pistol grip stock) to build a faux early WW2 Remington M1903. Barrel was new, never installed till I put it on the receiver.
I purchased two new early Remington M1903 smooth bolts at a Gun Store in Orange County. Both had the same bolt root stampings, one also had a R stamped on the bolt root. I used the none R stamped bolt to build the rifle. I figure the R stamped bolt would be worth more if I ever sold it as I would not have to prove it was a Remington early M1903.
These five shots were in the black, but the rifle would not hold the ten ring at 200 yards.
back in the day, to shoot a perfect score, all you had to do was hold the black.
Expectations that every M1903 would shoot sub MOA are unrealistic. That full length stock with a pressure point at the tip is a poor design for target shooting. However, they did that to put a bayonet on the thing. One real period problem was bullets. Modern match bullets have jackets with even sidewalls and are hollowpoints. It is my opinion that older bullets were not as concentric, so given the center of gravity was going to be outside the axis of rotation, they would wobble.
