George: the first pic clearly show the 'Field' stamp and the Hunter Arms Co proof mark which became standard after about 1922.
How an Armor steel Field brl ended up on a Specialty gun is only a guess now. It's possible that the Cody records might help http://www.lcsmith.org/shotguns/search.html
LC Smith stopped using damascus brls as a regular option in 1919, but they could still be special ordered thereafter, presumably until the supply ran out. Your gun was manufactured in 1920, so Tom's idea that the gun was re-barreled is certainly reasonable.

https://sites.google.com/a/damascusknowledge.com/www/home