Harry,
Some minor (off topic) corrections:
-The British Pattern 13 was the originator of this family of rifles. It was designed to fire a .276-caliber round. The British dropped it with the onset of WWI and had the Pattern 13 redesigned to take the .303 British, yielding the Pattern 14.
-When the US entered the war, the British contract for production of the Patter 14 was just winding down. The rifles were made by Winchester Repeating Arms in New Haven, CT, Remington, and a Remington subsidiary in Eddystone, PA (thus the WRA, RA, and ERA designations on the P-14's).
-To suppliment 1903 production, the Pattern 14 was modified again to run the .30-06 round. This resulted in the US Model of 1917 (technically wouldn't be a P1917 because the "P" for "Pattern" was British nomenclature, not US...but everyone knows what you're talking about if you call it a P17).
-The US gov't anticipated the War lasting well into 1919. As a result, the armistice saw the US attempt to withdraw from their contractual commitments to Winchester and Remington. Lawsuits were involved to force the government to honor the contracts. Remington was still left with an overrun of parts, and these were repurposed to spawn the Remington Model 30.
As for the PSP connection, I have heard nothing of that, so I can't comment on that end.