There are no original source descriptions that specify who was involved in making a barrel.
Based purely on photographic evidence, we do know that....

In England it would appear there was a master barrel maker with 1 to 2 apprentices / journeyman. If there were separate stations is not clear based on photographic evidence.

In Belgium there was always a master and journeyman or apprentice working on a barrel. This work was divided into several stages each with a separate team. The 1st team would twist and weld the billets. These ribbons were then wrapped around a mandrel. The 2nd team would take the coiled barrel and weld every joint again, shaping the barrel. The 3rd station would grind the barrel. The 4th station would fit the barrel. The 5th station would finish, i.e. apply the acid used to show the pattern.

Traditionally the starting point for an apprentice in Belgium was no where near a forge. When they moved up to actual barrel making their job was to pump the bellows and tend the forge. Every stroke of the hammer was dictated by the master maker. If some one has original source that indicates differently, I would love to see it.

As to the blown Baker. I am not sure how much honing, reaming, enlarging you can do to any barrel in the area of the chamber before it becomes unsafe. In Europe such an action would require reproof. I have posted a diagram of a barrel showing what were considered minimum wall thicknesses. I measured the damascus barrels I own, which all except 1 complies with that diagram.

I would suggest the fact it was damascus has nothing to do with the end of it. The reaming or honing does contribute but was not the cause. It merely confirms in my mind, that before any gun of this age can be fired, it should be examined by a competent gunsmith.

Pete