Get some Butches Bore Shine. It eats powder fouling very well. Get enough to put in a cup to soak your break. Can do this until its clean. For the crown, I soak a heavy shop towel and work the crown until its clean.
One thing you may want to try is a product called Break Saver. This is used mainly for the 50 BMG rifles to help limit carbon build up on the brakes from burning 215 to 230 gr of powder at relatively low pressures.
Brownells used to carry this but do not know if they still do.
There are two types I have seen, a light jell and a spray. Once the brake is totally clean you apply this product by either wiping it on for the jell or spraying it on. IT helps prevent the fouling being able to attach to the brake surface.
To be honest, this is a fact of life to some degree with a muzzle brake
so you can only try to control it as much as possible.