Let me see if I understand this correctly, your qualified gunsmith doesn't know enough to index the barrel in the lathe using a pin gauge ( tight fitted rod stuck into the bore to show were the center of the bore is ) the pin is usually made to fit the bore. Made in the lathe, not mass produced. then by using a 4 jaw chuck you center the bore in the lathe not the exterior. I would not have a lot of faith in your gun smith. I think you need to look for a different one or just take the leap and do your own work.

Personally I would have cut the barrel off with a hack saw then trued it by eye with a file then crowned it using a carriage bolt and lapping compound. That is if I didn't have a lathe. That was how I always did it in the past.