From Crossman's Book of The Springfield I learned that the receiver was made in 1935 (see page 34). 1935 was a year that Springfield only made 27,7259 receivers but not any complete rifles (see Brophy, page 425). No NRA Sporter rifles were made in 1935 but in 1938 twenty-nine were produced (see Brophy, page 427). However, your serial number is outside the block of serial #s shown by Brophy (1,406,315 to 1,408,446) for DCM sales of NRA Sporters (page 427). The other unusual feature is yours has a barrel band retaining spring, a feature not used in NRA Sporters but found on the much earlier International Match1921 "free rifles" which were heavy barrel target rifles (but your serial number puts it way past that era). Unlike your rifle, the "free rifles" had grasping grooves in the forearm (see Brophy 105-33).
The Circle P on the grip indicates the rifle was successfully proofed (See Canfield An Illustrated Guide to the '03 Springfield Service Rifle, page 33). The stamping on the stock below the magazine cutoff, SA/SPG in the rectangle indicates it was inspected by Springfield Armory's Stanley P. Gibbs (Canfield p 107). Unfortunately, Canfield's book neither covers the 1930s production of the rifle nor the sporter versions of the rifle.
That gas escape hole on the left hand side of the receiver is known as the Hatcher Hole, after (Gen.) Julian Hatcher. In event of a ruptured cartridge, gas could escape through this hole instead of back into the shooter's face.
I checked over Campbell's The '03 Era and found nothing on the '30s NRA sporters. He had plenty of information on the earlier sporters and target rifles.
Last, regarding the similar rifle, its serial # was 1,398,xxx and per the DCM paperwork it was picked up at the armory by the buyer, a colonel assigned to there. He paid $16.50 for it (because of the aforementioned defective/loose front sight).
Thank you for a most enjoyable thread. Like yourself I love research. Too bad there's no paperwork for your rifle.