brushing once with the dish soap actually seems to have made a difference very quickly, and it's sort of what i thought - some of the build-up came off (i'm not joking, it really did) and some of the rest of it got scrapy very quick. 

it's impossible for me to tell with my eye, as an untrained person, if it's a cavity or a stain. i need to be clear about that. i don't know.

but, much of it no longer looks like a cavity to me at all, once i softened up the plaque with the dish soap.

i'm not exactly recommending this. i don't actually know what the long term consequences are. but, ammonia is the historical toothpaste - it's what we used before we used toothpaste. and, it's easy to see why, actually trying it.