You need to be careful with bbls like that. It's like handling cartridge shotgun bbls and they will dent and crush easily in a vise.
Something as described already in form of a jaw that contours to the bbl shape is whats needed.
This may seem long, but it is a simple way of making a bench vise jaw for holding thin walled round barrels, mag tubes, straight or tapered and actually takes little time.
For use in a bench vise as opposed to a special bbl vise,,I'll take a piece of 4x4 and drill/bore a hole through it lengthwise just big enough for the bbl to pass..
The piece of 4x4 only needs to be 3 inches long perhaps a bit longer. Don't over do it. A bit brace can cut a large diameter hole quite quickly or a spade bit with an electric drill or drill press.
Keep it centered as best you can.
Once it's cut, put the bbl in the vise verticle. Put paste wax, or other non stick stuff on the bbl and slide the block down to the spot you want it to set while you work on it. Make it even with the top of the vise for convenience. A stub peg in the bore held in the vise is convenient at this point. Leave an inch or so of bbl showing away from the breech to the block for working area when you're tapping the threads later on.
Plug the bottom with anything from clay to paper towel keeping the bbl centered in the drilled hole.
I often make a cardboard disc that slides down the bbl in front of the block and jams into position there to seal it off.
Nothing fancy as long as it holds the block in the position you want and seals it off.
You can see that the need to cut the hole much bigger than necessary for the bbl to pass through isn't there. It just means more filler in the next step.
Mix up some epoxy. Stock bedding mtrl,, JB Weld, Bondo,,Anything that'll harden decently and pour it in the top opening (smaller end of the taper) around the bbl. Center the bbl in the hole again to make sure and let it harden up.
When it hardened,,knock the 4x4 block forward off the bbl. The taper and the non-stick coating will release it easily.
Mark the breech end of the block with some sort of mark so it covers both 'halves'
Now put the block back in the vise or on the band/table saw and cut it in two right down the middle lengthwise of the block. Making two halves. The saw kerf becomes the clearence for clamping.
The mark on the end makes for easy matching up the correct ends/taper.
Some 'smiths only cut one side of the block. Leaving the other solid. You don't have two separate pieces to manipulate (or get lost!) that way. I think the better clamping power is with the 2 separate pieces in my experience. Everyone to they're own way. If you've got bbl sights, bbl pin attachments, ect to deal with,,the 2 pieces is the only way.
Clean the bbl off squeeky clean,,dust with rosin if you have it. A bit of plain white confectionary suger works very well too if you want to go very old school. Maybe that's middle school,,,
Put the two halves of the block around the bbl in the right place and position. Place it in the bench vise and tighten it down and go to work.
Mark the blocks with the bbl style &type. As you accumulate others, you'll be able to keep them separated and matched up.