Oops, sorry I missed your actual question. I don't think the minimum bore to thread wall thickness was addressed in the book. I'll look through it again and see if it does. If not, a call or e-mail to Troy would give an answer as to what his opinion would be. He is very helpful with questions when you can get him.
The major dia of 9/16 thread is .5625-.338 bore=.2245 total wall thickness. .1123 per side. I don't know if that is good or bad. You certainly wouldn't want a thread relief and would want a radius on the barrel shoulder. A shoulder on the barrel matching a counter bore at the back of the brake would probably be helpful too. On the index bushing thread Stiller did some strength calcs with stacked tenon to bushing to action strengths which should apply here. If the thread fit was say a tight class 3 and you used a finer pitch say 32 TPI I would think it would be plenty strong enough but would the pressure be high enough to expand the bore/brake at the muzzle? Probably no more than the original barrel. A common threaded muzzle is an AR15 with 1/2x28 thread. .5 thread-.224 bore =.277 wall. .1385 per side. .0262 per side difference from AR to your .338 a fair amount. Looking back to the beginning of this thread with the barrel dia of .550 and .308 bore which had .121 per side wall thickness many said this was safe. Maybe someone else will have an opinion on whether your situation is good or bad.