Threaded barrel on LTR- keeping it clean?

[45Badger]

The bore is easy

I've got a thread protector, but the threads (on barrel and protector) are "in the white". Unless I take it off and clean it every time I shoot, gunk builds up in the crevices of the thread. Brown/rusty gunk is not what I want. I'm thinking a flash suppressor might be the answer. Any good ideas to improve the situation?

Thanks!