Here's another thread on barrel fabrication & profiling -
6" .30 Luger barrel, 1900 style
http://forum.lugerforum.com/showthread.php?t=29518
Sometimes you get ahead of yourself...Which is what I did here...I left the muzzle nice & long to chuck it, but forgot that I needed to finish the muzzle [turn to dia, round, and crown] before milling the sight bases round...So I had to cut the excess off and finish the muzzle...
I used a 4-jaw chuck. Took about a half-hour to get the barrel centered.
I don't recommend this setup; I don't like the end being unsupported while it is being turned, but due to CRS it turned out this way. I took very small cuts and slow manual feed, and it turned out OK.
The centering in the 4-jaw is a PITA. It has taken me an hour in the past, to get it down to +- .001". This time I clamped a 7.6mm ground pin in my tailstock Jacob's chuck and hung the barrel on that, and ran the jaws of the lathe chuck up to the barrel for a rough centering. Then it was just all trial & error with the dial indicator to get it 'just right'...