I wouldn't chop it up either.........
As far as it being worth anything....You'd probably have to look at the serial number.....
Rem started they're original 1903 at3,000,000 so as not to confuse with Springfield Army....
I am not sure what what the last no. waswhenREM recieved permission
from the Government to start modifying the gun..
I would guess that the .303 British (A Prototype) that RemingtonArmsmade in the Model 1903-type for Great Britain, (after war was declared) WOULD BE WORTH QUITE A BIT OF MONEY......

The initial production of the Rem Model 1903's are identical to the 1903 made by Springfield Army......Very well made as good as me custom built rifles.....Probably Worth Quite A Bit......
Than as the war went on Rem had to cut minor corners to keep up with demands for production.....
During the War, TWO, 1903A3's (modified 1903)Models were made by 2 different Companies...Smith-Corona (the Type Writing Company) and Remington...... I think Smith Corona had their name stamped on the barrel.