I've broke in quite a few Brux barrels.
Shoot and clean after each shot for 3-5 bullets.
Shoot 5 and clean, once or twice.
No brushes needed, just a patch of bore tech eliminator down the bore every 15 minutes, about 7-8 patches do it the first couple shots 5-6 the later in the cycle. I always run a damp patch of Kroil thru the barrel after cleaning, not dripping and soaking just damp to leave a thin film in the bore.
That should brake in 95% of them for sure.
Some will be broke in after 3 shoot and cleans, at least that is my experience. The stuborn ones may be rough in the throat, that could be a reamer issue, that the smith should address.
The higher intensity chamberings seem to take a couple more shoot and cleans, as compared to the cartriges that drive less than 2900 fps.
My personal 260 build, was 1st shoot and clean, 2nd shoot and clean, next 5 into .315" off a bipod and rear bag. 2 patches and no copper in the bore.