IMHO DO A CHAMBER CAST.AND SLUG THE BARREL. The german gun collectors assn. can give you lots of information on your Simpson.
The Simpson story is quite interesting. A Jewish family busness
that made high quality guns. They were forced out by the Nazis. many of the family are in the USA. The Simpson name was still attached to some guns made in east Germany after the war and might still be. Most likely Your drilling has A buffalo horn
trigger guard and butplate. BP Proof ?