Your rifle s/n 3412978 is one of about 200 recorded in the CMPicon inventory in 1999. It is also recorded in the Records of the Springfield Research Service (SRS) noting the CMP inventory status.
For a charge of $25.00 CMP will search their records and may be able to provided some additional information. SRS can also provide additional information but if all they have is the CMP inventory I doubt it would be worth the cost.

The rifle appears to have a June 43 Barrel which is appropriate for that s/n. The barrel also has a mark at 6 o'clock which suggests its original.

The boxed "OG" stamp suggests the rifle was rebuilt at Ogden Arsenal.
The Bolt has been parkerized which is typical for a rebuild /refinish.
The magazine box Assembly has also been parkerized. Originally it was blued.

The firing pin is from an M1903.

The telescopic sight is a very late model M73B1, so while correct, it is not original to the rifle. (CMP records may disclose if the rifle was shipped with a scope.)

Questions:
1. Are there any stamps on the left side of the stock above sand behind the trigger. Specifically a large "RA", an "FJA" (boxed or unboxed) and the "ordnance escutcheon"?
The stamps may be faint but without them i believe the sub-inspectors marks forward of the magazine might be counterfeit.

2. Is the barrel 2 or 4 grooves?

Regards,

Jim