I always like to go to the people who were there. The London Illustrated News went to a factory making Enfield rifle barrels, scratched some excellent engravings of the various processes, rolling the barrels looked very exciting if a bit frantic. They said it was Marshall's iron. Later I saw an excavation of Marshall's factory and they were making crucible steel. The notion that damascus needs to be wrapped around a core is not mine.
Ah yes, I know that article.. The whole business of making barrels was, as you say, a bit spectacular and not that healthy for the participants!
I think you are at risk of making two and two equal five in your conclusions of what was happening at Marshall's ironworks. From what I understand, Marshall was mostly a puddler, making wrought iron by the Onions process. They also seem to have had a crucible furnace as this was a follow on process to making wrought iron, but as I said, I would be surprised if the steel made in these furnaces went into Enfield barrels. I can see crucible steel being used in making twisted laminate barrels for the sporting trade, but not for military barrels. There was not the wide choice of alloy steels that came into existence in the following century after the chemistry and metallurgy became better understood. Mostly all you had was cast iron, which was then worked into wrought iron by burning off the carbon, and blister steel made by putting some carbon back into wrought iron by heating in charcoal filled boxes. Crucible steel was simply blister steel melted in ceramic pots at the highest temperature they could achieve. The limiting factor was the ability of the crucible to stand the heat. The crucibles only held a few pounds of metal and could only survive a couple of firings. It was not actually possible to melt large quantities of most steel alloys until the beginning of the 19th C. the best you could achieve was a pasty mass for forging etc..
You need to be a bit careful about using articles from publications like the LIN which was always more of a public entertainment than an academic journal. I am sure the writer meant well, but would not have spent that much time ensuring his copy was technically accurate. Better references can be found in more obscure academic and engineering publications, but much of this information was treated as private commercial secrets at the time, and hence very difficult to authenticate. There was no real definitive terms for sub types of metal, and many materials were known more by who made them rather than absolute chemical or physical characteristics.
We still see echoes of this in terms such as Babbett metal, Gunmetal, Stubb's Silver Steel ( "Drill Rod" in the states). There is not actually a technical difference between "Brass" and "Bronze" as many alloys contain both copper, tin and zinc..!
I suppose what I am saying is that it is probably pointless to make definitive statements about metals produced before the 1920s. Much of what was produced in those days was dependant on the skill and judgement of those making the objects at the time, with much emphasis on trusted sources of supply. It is only comparatively recently that engineers and designers have been able to specify and select standard materials based on more scientific assays and testing regimes. There are many however who say that there is much in material science we have still to discover...!