That is an excellent book. It was prepared originally for bidders on a contract to manufacture the M1903 for the Army. The Army decided instead to contract with the companies already making the Pattern 1914 for the British and have them make the rifle in .30-'06 as the U.S. Model 1917, so no private company ever made the M1903.
Reading that book will open the eyes of some folks who think they know how things were done back then but are wrong.
As to serial numbers, there is no source for M1903 or M1 rifle or M1 carbine serial numbers beyond a very few. Springfield Research Service was able to trace a few serial numbers but not any significant percentage. Also, their records provide only a "snapshot" in time. If a company inventory that has somehow survived shows Springfield M1903 rifle 876543 in the arms room of Co.A, 999th Regiment, 777th Division on January 14, 1923, that does not prove who had it in WWII or if your great uncle carried it in 1937.