Stocks are usually about a year earlier than the receivers. They have a drying time. That's not a date on the barrel. Most of the others are inspection marks. That is a date on the bolt and since your bolt serial matches is probably original to the rifle. The P typically does indicate private sale but I believe they put that in front of the serial number, not on the barrel where it is. But, that could be what it is. It matches no inspection marks I can find.
My K31 was made in 1941 and sits in an October 1941 stock.