Hi Dave,
I think part of the problem is that most of us use the term "Damascus" barrel kind of loosely. I am not sure any barrels made by Europeans regardless of age were real Damascus steel. That process disappeared from the Middle East sometime in the 18th century. There were all kinds of pattern welded barrels made and many before 1810. Twigg, Mortimer, the Mantons, Nock, Egg all made fowlers with patterned welded barrels in the last quarter of the 18th century. Many were called "stub wist" and were made (I believe) from horseshoe nails. Of course, continental gunmakers used pattern welded and twisted wire barrels for many years, particularly on fancy rifles. During the 17th and 18th centuries Spanish and Portugese steel barrels were probably the best in the world. Many English gunsmith made fowlers for clients using those Spanish barrels. They were highly prized. I don't think any of the pattern welded barrels at the time were superior to the Spanish barrels in any way and the twist pattern was really just an expensive cosmetic feature, although there is no question that stub twist barrels were excellent. Later in the 19th century, steel became much more widely available and I'll bet barrel makers increased their production of pattern welded barrels because they could get the steel to add to the soft iron more cheaply. They could then gratify the demand for pretty pattern welded barrels at a lower cost. Hence, more fowler barrels were pattern welded. Anyway, that is my speculative answer to your question. Of course I could be way off the mark.
dave