They make a ventless Boss. Lots of folks don't mind the recoil and don't want the noise and muzzle blast of the brake, so they came up with one that still functions as a barrel tuner but is solid along the sides.
Caps, I don't know about. You could buy a spare BOSS lock nut and just shoot with two lock nuts on. That will protect the thread.
My thread gauge and my micrometer show 24 TPI and 0.561" major OD on my mid-90's Browning A-bolt. That would appear to fit just inside 9/16-24, but 0.0015" is too tight for commercial threads. 5/8-24, the next commercial size up, is too loose. I'm going to guess the one on my Browning is meant to be a 0.575-24 thread. I base that on a commercial thread crest that is 70-80% of sin60°*/24" at the crest. If that's right, then about 0.014"-0.021" needs to be added to the diameters of the barrels to find rated thread OD. That works out to 0.575" pretty closely for me and makes yours look like it was intended to be 0.6-24. I bought mine circa 1995, and they may have changed it since then?
Anyway, if you are sure of your 0.581" reading, I would start with a 0.535" hole on a lathe and and run the internal threading bar in until you can screw it onto the barrel. If you mistyped and have 0.561" thread OD on your muzzle, as I do, then you want a hole 0.515" to start internal threading.