I did one of these a while back but used a different technique I had a press fit SKS barrel (new) that I bought from sarco inc when they had them cheap. 3/4-16 Threads were cut on this, about an inch and a half long. I removed the original barrel from the action on the carcano with much effort and a lot of penetrating oil... my home made action and barrel wrenches were a little undersized. next, the barrel was cut off, leaving at stub and the threads. maybe an 3/4 or 1 inch of the old barrel was left in order to make it easy to remove again if needed. this was chucked in the lathe with copper wire wrapped in the threads to keep them from getting crushed by the jaws. I centered the barrel stub as well as I could (it had been bored out and re-sleeved by the italians in about 1924), using whatever original concentric surfaces available. I bored out the barrel stub on the lathe, then used a 3/4 - 16 tap to cut the internal threads, since this was much easier than trying to single point with such a small hole. I made a barrel nut out of 1" 4140 steel hex rod that I had laying about in my shop, and tapped it in the lathe also. this locks the barrel tight into the barrel stub after headspacing.
I probably should have bought gages, but I just took a sampling of live rounds, and put a piece of scotch tape on the back (maybe two??), and tightened the barrel into the action (firing pin removed from bolt), until it was hard to close the bolt, then backed it off just a hair until it closed easily again. tightened down the barrel locking nut, and it was good to go.
I took it to a friend's farm and put a round in with just the primer, no bullet. got it tied to his shooting bench, and then went behind a tree with a long string. ping! worked well enough. primer looked o.k., so I put in a live round, and fired that down range from behind my tree. that case and primer looked fine, so I shouldered it... was a beauty to fire.
since then I've been busy trying to get other stuff done, and haven't put any sights on yet, but that is in the works in the next few weeks. all told, I have about $160 in this, it was a fun project. still looking to install the single stack ak mag, or otherwise modify so I can use the en bloc clips from the bottom.