That was an early Remington turn bolt sporting rifle, made in the period between WW-1 and WW-2 when Remington didn't have war contracts. I really didn't know that The PSP was using them.
They were made as new rifles (not a converted sportsterized cut down) from Eddystone P1917 Enfield. the action design started design life as a 303 brit with the english, but when the war in Europe broke out and england needed help, they transfer the manufacture here. Then the adapted it to the 30-06 cartridge when the USA enterred WW-1 and needed more guns than the Springfield 1903 could be made. After the War-1 Rem had parts and there was interest in bolt action sporting rifles from people that returned as soldiers in Europe. So Rem used the military action and commerical barrels with decent walnut stocks, sold as the Remington Model 30. Still had an ugly looking action with a "pregnat looking" magazine belly. the ultra ugly bolt handle, dog legged was there also.
They mad them in their line of remington rimless shells 25 remington (same as 25-35 but no rim), 30 remington (same as 30-30 but no rim) and the 35 Remington. Also they chambered it if I remember in 30-06 (most popular) and the 7x57 and the 8x57. Like all 1917 Enfields the action is LONG. So there were some made or converted to 300 H&H and maybe also some 375 H&H floating around.
They were popular, but some what expensive for the depression era. so only the wealthy bought them (and I guess the PSP?); because of this the ones I see at gun shows are in really good shape. it had to compete with the surplus 03s which the government was disposing of super cheap.
The ugly bolt was finally dropped and the model was called the 720. later the action was redesigned as the more popular 721 a totally new action and the parent of the m700.
Interesting to me is the M700 has retained the same style safety lever design as that old Enfield rifle with the thumb piece just thinned out a little.
The M70 Winchester safety has decended from the Springfield bolt mounted wing safety.
-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.