I've not chambered a barrel in the steady rest, but if I was going to do it, this is how I'd do it assuming I was starting with a new barrel blank fresh from the barrel manufacturer:
The new barrel blank should already have a 60 degree cone in the bore at the muzzle and breech. Install the barrel between centers with the muzzle on the tailstock end and machine the OD of 3/4" or so of the muzzle round which will also be concentric with the bore. Reverse the barrel in the lathe and take a light cut on the breech end to make the OD concentric with the bore.
Cut the usual inch off the breech of the barrel blank to get past the part of the bore that is probably oversize due to lapping.
When you put the breech in the steady, you can use your 4J to hold the muzzle and use this newly machined surface to center it in the chuck which will also center the bore.
Then center the breech using a range rod as Kirby suggests. You will only need one range rod per caliber, but you may need several bushings depending on the actual bore size.
When the machine work (tenon and chamber) on the breech of the barrel is completed, make a thread protector as you suggest.
Saw the muzzle end off past the trued surface, reverse the barrel in the lathe, center the thread protector in the 4J, use the range rod to centered the muzzle in the steady rest, then machine the crown, install a muzzle brake