Randy, you got me!!! LOL.... You are right, because the "carved end" is not getting finished it could be done BCB! Geesh and me of all people missed that!
By the way, some of the rough shaping could be done on a band saw too.
I wonder if it was turned straight, just how much steam it it would take to bend it? If a wooden plug was made to fit the horn to keep it round, a jig could be made to try to bend the shaft. That would be an awesome way to do this idea. It's small enough to steam in a pot and a 1/4" rod could fit inside the pen to strengthen the tube and provide leverage.