My method of working between centers is the best I can do since I cannot run the barrel through the headstock. The tenon and the barrel beyond the tenon are worked with reference to the center, then on the steadyrest which was set and run smoothly with the barrel on centers. The reamer seeks the center of rotation. I do not see a better way using my lathe (not a gunsmith lathe with a large headstock bore). I make ACCURATE barrels.