I have seen two gun like the one you describe. One was a hammer 12 and the second was a hammerless 16, both with damascus barrels. Both were mid quality guns, not a best quality gun, but much above the average JABC. But they were not hand made guns by any means. They were in fact well named. Not as machine made as the old Remington 1100, but much more than other doubles of the day. Like a gun I have that is the "Interchangable" meaning that parts from one should, could, or at least might fit another.
At one time claiming to be machine made meant the latest in modern manufacturing methods had been used and it was considered a step up from hand made. Machine made shirts were deemed to be a higher quality than home made or hand made shirts. Funny how things are now machine made and hand made have just the oposite meaning.
Often we see engraving and think about how much that would cost to do today. Back when that gun was made the engraving was a minor cost. I have read that a middle grade gun could be engraved for several dollars in those days. Gold band or wire would have been fairly cheap to have done. Maybe 50 cents worth of gold and another 50 labor to do the inlay.
Post pictures and please show the proof marks on the barrels and water table. Others here should be able to give you a ball bark figur when your gun was made. The two I mentioned were most likely made between 1900 and 1915 from a quick look at the proofs. BICBW-again.
