dweber49, The Simon/Samuel confusion seems to come from both men living in Hamburg, Pa. but at different times.
According to Sellers American Gunsmiths book, Simon Miller lived in Hamburg 1775-1806. Samuel Miller was there in 1823-1849. Now, I'm not sure these dates are the gospel no-doubt-about-it truth, but that was Sellers research at the time.
Also, your rifle might well be an originally percussion gun, and never a flint, so would be a product of the later Samuel and not the earlier Simon. I say that because from the pictures it looks like your gun is missing the 'notch' in the stock usually found behind the flint cock, that wasn't required by the differently shaped percussion hammer. Look at the link from Seth I, the picture of the lock, and notice the gouge behind the flint cock. Your gun looks like it has a burned area there, from the percussion caps, but not the flint sort of notch found on those guns.
The outside of the lock plate has some filled holes, maybe from a frizzen spring, but also has engraving around the nose of the plate. A picture of the inside of the lock plate might show if it was originally a flint.
Either way it's a nice gun and a nice example and thanks for posting up the pictures for us.
John