Dustin,
To my knowledge, no one has used damasteel to produce shotgun barrels of any type. Oscar Gaddy and I had many discussions on this topic. We eventually decided to take on the project. Oscar had a M21 that had been through a fire. He was going to retemper the action. It was left to me to find the barrels. After many attempts, we had to give it up. I could not find a supplier for the blank tubes. The American supplier was unable to acquire stock of the correct dimensions. I even called Sweden and spoke to some one at Damasteel about this. They were not interested in a "one of" type of project at the time.
Originally the goal of forge welded damascus was to reproduce the inherent strength of Wootz steel. The early fluid steel was plagued by imperfections and was not very capable of handling the pressures of gun powder. Eventually forge welded tubes came into use. They provided a cheap alternative to the hard to acquire Wootz. They were able to handle the pressures if the barrel walls were thin. They were light enough that carrying a sxs was not an exercise in brute strength and stamina.
Bessemer and then Whitworth found ways to decrease imperfections and increase strength. Despite this damascus remained a popular choice.
The knowledge and skill to produce forge welded damascus was never really lost. It did fade, being left mostly in the hands of a very few gunsmiths and a few zealous aficionados. It has been "rediscovered" a great many times.
In Europe there have been and still are some individuals who can produce forge welded damascus. Some are able to reproduce the old patterns at will. Some can not produce those patterns. I know of English, French, German and American gun / blade makers who have done it.
Pete