I knew my eyes were bad (in fact I have an appointment in less than an hour to discuss cataract surgery) but I can't see any of the markings on your rifle barrel! I do see what appears to be a plugged screw hole just toward the muzzle from the vertical line. The line might be the remains of a sight cut or pressure mark, and the screw hole part of the sight mounting.
Have you tried making a rubbing? Actually, your drawings are probably the best that can be done, but another detail or two which just look like part of the 200 years of dings might show up in a rubbing.
