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The centers are used to set up the steady rest either on a spider (octagon barrel) or direct on a round barrel, then the crown is cut. If you ever have occasion to set up a barrel in a head stock of a lathe, dial indicate both ends to center ( without the breech plug installed) run at a slow RPM and look down the bore. It will at times look like a jump rope the bore can be so crooked. That is the reason for orientating them in the vertical plane so the sights can more easily compensate for the runout. That is also the reason deep hole boring well/accurately with minimum runout is the real secret of a good barrel with the rifling itself being the next most important, in my opinion."Barrels are never bored perfectly straight so even if you set up between centers (which is the most accurate method) the crown will not be absolutely square to the bore axis but is as close as you can get it in a lathe and you will never be able to detect any difference."
I don't understand how you would cut a crown with centers inserted in both ends of the barrel.
I use a tailstock spider to make the bore run true. I use a close fitting long arbor to get a couple of readings over a length to be sure the bore is centered and true.
A piloted reamer would also do just fine. It would tend to self enter.
It does not need to be dead nuts perfect.