There is a bacteria in them that eats that larvae at least. Look for BTi (bacillus thuringiensis subspecies israelensis). Dunno if it works on the mites, but it will work on fungus gnats larva.
It's in most tea inoculations great white/mycogrow/orca etc.
Just saw that you said it didn't work, there's always a possibility the colony wasn't large or mature enough or that it wasn't present to begin with in the tea. But either way I feel like none of the organic solutions are 100%, aside from drowning/heat/suffocation which aren't always reasonable for your situation or particularly good for your plants.
I'm in the northeast and I don't know anyone that's had russet mites out here so I can't speak much on those.
