It's too hot to work outside, so I just pulled up INSPECTORS'S MARKS in an old Dixie Gun Works catalog. The stamping "JM " was used by the armory sub inspector Justin Murphy. In the period 1813 through 1833, he inspected guns at Jennings, Pomeroy, Starr, etc, etc, etc, so identifying the original Model 1816's gun maker is pretty doubtful.