Try adding baking soda?
Discussion
I did not try that. How does that work?
It's a mild abrasive and other properties that help keep the mouth gross away.
Easiest is a 1:1 water/baking soda paste, but there other things you can add in for taste ( it taste pretty awful ) like a drop of peppermint oil.
There are probably baking soda toothpastes out there with that