BP shotshells are a hoot, to be sure. Two things:

I've had much better luck doing the initial cleaning with plain _cold_ water, both for barrels and brass cases, particularly the latter which will stain in hot water. After the main part of the goo is gone, hot water through the barrels will help dry them when you mop up.

Take a glove along when you shoot - those barrels get HOTHOTHOT right now!

OK, three things. MagTech brass cases work well but it's thin enough that you need 11 gauge wads. RMC turned brass is wonderfully durable, if somewhat dear, and is as thick as a plastic or paper shell so 12 gauge wads work fine. Plastic wads make an unbelievable mess in barrels with BP.