Hi Bob,
According to Charles Clawson's book, it's a Springfield Armory barrel produced prior to 1943 when they added the Heat Lot number above the "S" and "P" stamps. Guessing a replacement during rebuild at SA but some Colt and Springfield Armory barrels were used in early Remington Rand production so could be original. If it was in the bin, they used it. The "S" is a provisional civilian ordnance inspector's mark from W.E. Strong. The "P" is a firing proof. You're correct. The pistol was produced in mid-late 1944.
Brian