The book you probably want is "Fighting Iron" by the late Art Gogan. The subject, as least regarding shotgun barrels, is also discussed in "The Gun" by W.W. Greener. There is a reprint of his 10th edition out there but I prefer (as far as this subject is concerned) the 1st edition, by his father, W. Greener. I downloaded that from google books but they probably don't allow that any longer.
That said, you probably have a B'ham made gun and, as such, virtually all of the parts were made by specialists. This was true, if primitive, mass production. Each worker made only one or two small parts and they made them to established sizes with specialized tools. This practice goes back to at least the 18th century and probably to the 17th century. Thus... there will be no identifiable features that can be associated with a particular workman. The name on a gun is invariably that of the person who organized making it or of the dealer who ordered it. We've practically no specific knowledge of any of the people who physically made or decorated the bits and each gun probably includes the work of dozens of individuals.