If the barrels are not thick enough at the muzzle to get a proper shoulder for 9/16 threads (ie 0.662" before cutting), then I recommend getting the CB mount with a face mounted brake.
If this photo is representative of reality,
A 5-lb., bolt-action sporter from the king of tactical big-bores? In case you didn’t know, the Barrett family likes to hunt, and the new Fieldcraft rifles are made by the same workers and on the same machines that produce the big M82A1s and M107s.
www.americanrifleman.org
their threads do not have a proper undercut.