★★★★☆
So I started my online research. The one thing I came upon time and again (that wasn't very expensive and that I already have in the house) was Dr. Bronner's liquid soap. Those who reported using it said it would SLOWLY wear the tartar away. I've brushed with it before in a pinch so the taste wasn't unknown to me. I was willing to try again. I'm happy to say that so far it's been working, and yes, slowly like everyone said. It really just depends on how much tartar is involved and (I guess) how old the tartar is.
It's been about 2 weeks now, brushing with one drop of the peppermint liquid soap at least twice a day. It makes a LOT of suds. My teeth feel silky and clean. I have also ordered a food grade peroxide to rinse with. I wish I could have taken pictures before I started up to now. But how in the world would I have gotten the camera into my mouth???
I am so thankful because I don't want another bloody dental cleaning, caused by the girl having to scrape sections where the ultrasonic didn't work well enough. Will post more in another week or two.