Lloyd 3,
You are correct that the modifications to the Springfield resulting in the 1903-A3 were to speed up wartime production. Other than finish, the major differences were the use of stamped parts in stock hardware and the bottom metal. A major improvement was changing to an aperture rear sight ( some might disagree), attached by a dovetail milled into the receiver bridge. DCM sold a great many, both 1903 and 1903-A3 to NRA members for a very attractive price ( as I remember $15) in the 1960s. They sold them later, but after the Clintons tried to stop the program, prices went way up. The 308 Norma didn't lose out to 300 Win. because it wasn't a great cartridge, but because 300 Win. was available in American rifles and Ammo was more common. The American Rifleman ran articles describing different ways to "sporterize" these rifles. I think it would be good to save some of your father in laws ammo as keepsakes for your son, it was loaded by his granddad's hands. Your idea that your father-in-law likely used either 4350 or 4831 has merit, but another possibility is Norma 205 which was replaced by Norma MRP. It sounds like your son will not only have his granddad's rifle, but will cherish learning to load for it with his dad. Good on you too.
Mike