I would be more inclined to believe the "P" is more likely to be an indication that the barrel had been proofed. I think it unlikely that a treaty rifle of that time period would be .36 cal. Just for starters. The gun is of very high quality, and not at all garish in its decorations, which again leads me to believe it wasn't made for a Native American. JMO, everybody's got one.
Hungry Horse