AX10AVIATOR, the double heat treat started about 800,000 in 1918, your serial number indicates in was made in 1909, with a barrel stamped 1922, the barrel could have been installed anytime after that, the rifle should have been blued. It would appear you need the stock, upper wood, front band and rear sight, then someone would say the parts are not 'correct for the year' and or it is a rebuild, all of this has an effect on the price, after getting it back to a military configuration the price would be between from $400.00 to $6500.00, you could spend $200.00 for the parts. There was an attempt to make a carbine, bad news, I believe there were only two made. All of my 03s have scopes and after market stocks except one, it is a Remington 03 before A3, I have a Norma 308 Mag barrel that was removed from an A3A4, I have not decided yet.
Without having the history of your receiver, there is no way to determine how many rounds went through it before the barrel was replaced, seems Springfield was unaware other countries were manufacturing rifles, at about the same time the 03 was being developed, the Japanese built the T38 6.5X50 with an outstanding gas escape system, Mauser before the 03 built and designed the M98 with a gas escape system, the Springfield was fitted with a gas escape system that was named 'the Hatcher hole' not the Springfield Hole.
The cone faced barrel looks very similar to a shaped charged device, there are a lot of excuses, Hatcher recommended the Low Number rifles be taken out of service and replaced, to say Hatcher did not find a reason for saying that is a conflict when someone says he only found fault with a few, there are was an offer to replace all low numbers with high number and or Remington receivers, some claim they dropped the receiver and it shattered others claim they hit the receiver with a hammer with the same results, the low number receiver shattered.
As a side not, Winchester/Browning introduce nickel steel in the Model 94 in 1895, Springfield discovered nickel steel in 1927, 32 years after Browning and Winchester, Rock Island and Springfield manufactured 1,000,000 rifles that put the shooter at risk of injury.