Your A3 is not in any way related to an A4. There has been a fair amount of erroneous speculation and falsehoods posted. I feel sorry for the OP who has to sort this out. I suggested a book, No go. I will now suggest the GunBoards forum and CMP forum.
All 03 bolt handles are curved down. The question is has this bolt been modified for a scope? If yes, then a new "R" bolt body can be found for short money. Very easy. Why guess?
The "block" on the butt stock is a cheek piece for use with a scope. Agreed that has to go! The OP needs to remove the handguard and see if the current barrel is drilled and tapped for scope blocks.
If I am reading all the above talk and pics right, 3,599,xxx is around April 1943 (did I see a 1944 post?)
https://www.remingtonsociety.org/1903-and-1903a3-production-and-serial-no-table/
