Raimey: PLEASE don't take any of my words as confirmation of anything.
I was born in 1945, and wasn't there when these commercial activites went down. My "information" is speculation, "connecting dots", reading in my Double Gun Journals, and listening to the "adults" on this most wonderful BBS. Also, in part of former career, I was instructed in business, manufacturing, retailing and industrial relations. I find the history of firearm manufacturing companies most interesting....and very repetitive regardless of country or continent. I think it is very predictable how companies operated based on economic (and sometimes, national-political) factors affecting them at the time.
I can't answer your question about Kirkwood and Mauser variants - as I simply don't know. Early company catalogs will hold the answer of offered items - ideally confirmed by in hand inspection of suitably marked "goods". The problem with inspecting "goods in hand" is the question - "How do I know this item is original and unaltered?".
More speculation for you - Regarding the business of US companies IMPORTING shotgun tubes/barrels. I suspect that individual American companies did not deal with steel manufacturers. I suspect they dealt with American or off-shore "middleman" companies, or individuals who represented a number of companies, who offered a variety of barrel metal and barrels based on real or imagined quality and PRICE. Father and son Houchins make a fine case in the Spring 2005 issue of Double Gun Journal that for AMERICAN MADE steel LC Smith/Hunter Arms was dealing directly with Crucible Steel Company and then Holcomb Steel company of Syracuse NY for their steel barrels. I have heard it argued that these Syracuse companies provided only the barrel steel, and that the steel was later re-worked into barrels. I don't know. For very basic economic reasons, I suspect other American gun makers did the same as LC Smith/Hunter Arms and bought the least expensive steel available FROM WHEREVER for their general production at that particular moment. The higher grade models offered by some companies sported "expensive" steel names such as Whitworth and Krupp and were priced accordingly.
Further speculation: - Regardless of whether the "middleman" was American or foreign, - whatever his nationality, I'm fairly certain that PRE-1900, much of what they offered to American (and some British) gun makers originated in Liège (regardless of what trademark was on/in the metal. The counterfeiting of goods is not just a recent Chinese phenomenem - especially when the goods were destined for a country without its own proof house). I base this opinion on the fact that PRICE drove (drives) nearly everything - and "money talks".
Offered FWIW - Just my $0.02, and hope I'm not just occupying bandwidth.