Bill Fiorini was a fantastic smith.
Having watched the old documentary video "Making Damascus barrels", I don't think the process is unobtainable now. One of the challenges that would be faced is the stuborness of modern steels compared to the steel/iron mix used in the old barrels.
Watching the way the steel moved under the hammer and when it was being twisted in the video tells me it was much more ductile than what I am used to forging ( all tool steel ). That being said, the right mix of steels to produce a strong barrel but one that is forgeable without so much difficulty would be a key to sucess. Steels like 4140 have an air hardening quality that can be a real pain to deal with.
A mix I would try might be 203E and 1018 with a 4140 core. One issue is wrapping the ribbon around the core and dealing with scale on the inside of the ribbon that would end up trapped. Perhaps a tapered core could be used and once the ribbon is wound, the core could be removed so the scale could be removed and then reinsert the core and finish welding it up. The barrels are obviously tapered anyway so it may save a little machine time in cleaning up the barrel.