1254780 fits into a small group of National Match 1903s consisting of 1254770, 778, 789, 791, and 801. Your photo appears to show the right receiver rail polished, are both rails polished? Yours may, might, could be an undocumented NM?
Do you have the stock and bolt?
An original NM barrel (or any service grade 1903 barrel)should show the two slots where the rear sight collar was pinned on. I'm not seeing this on your barrel, it would have to be turned down to remove evidence of the two pins. This was commonly done, even Griffin and Howe would do this! If it was turned down, the portion mating with the receiver would be smaller in diameter that an original barrel. If it's not turned down, it should be a Sporter barrel. Sporter barrels have a slightly different contour than service grade barrels.
One last thought, Springfield Armory 1923 serial numbers ranged from 1252387 to 1261486. 1254780 should be fairly early in 1923, the barrel dated 8-23 seems a little late to me. It might not be original to the receiver?
HTH
