Hi dayspringfarm. I replied via PM. Best wishes.
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Actually, I believe neem oil does work. I agree, don't use tea tree oil. Pyrethrins will work and this is I believe a "natural" remedy, but they are active only for a short period of time as they break down in light, if I remember correctly. A pyrethrin/permethrin mix is fairly effective, commonly available as poultry dust or flea and tick spray, and from what I've read, a much less "serious" chemical than Sevin. Some use flea preventive drops for dogs and cats with good results. You would have to research this, but I believe this is not an insecticide as such. DE will not resolve the problem.
I honestly don't know of any natural ways to get rid of mites, I ended up using proynl, which is a cheaper version of frontline, and putting it on all twenty something of my birds. got rid of them within the day!