I make my own brakes, so on the thinner barrels, I make them with 9/16X32 thread so I have thicker walls. For your For your application with a barrel already threaded, if you can try to find a smith or machninest who can make a counter bored brake that fits over the barrel and butts up up against the muzzle. I make the brake body, bore it out .020" larger than the bullet, bore it out and thread it. then, I'll counter bore it so fits over the muzzle about 1/2", leaving at least 5/8" of threads. I taper the brake so it blends in with the barrel. Then I screw it onto the barrel, then I set it up on a mill to drill the ports. I only work on my own guns. I don't want the responsibility of working on other peoples guns. on the lathe I use now I have to remove the barrel. It's a lot easier if you have a lathe with a short gear head so you can leave the barrel on. The plus side is when I remove the barrel, I'll true the reciever face, and lap the bolt recoil lugs to the reciever. I've gotten amazingly better shooting rifles by doing that.
Good luck.