The CMPmight be able to give you the basic information you have from Promo's post above. You can write to Springfield Research Service (the organization that has the information), and you can probably get a copy of the receipt showing who the rifle was sold to. Doing it is a little costly and time-consuming. You have to subscribe to their magazine, which I believe is $35 a year and pay something like $50-75 for a letter of authenticity and a photocopy of the receipt.
By the way, your receiver originally started out at Rock Island Arsenal in 1919. Virtually all receivers with serial numbers in the 1,289,000-1,301,000 range were made off of forgings and blanks from Rock Island Arsenal, which produced M1903s from 1904 to 1913, and again, from 1917-1919.
Here's a picture of my NRA Sporter, which was modified by Griffin and Howe, sometime in the 1930s. Serial number 1,295,379.
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