I know I'm going to get a lot of flack for suggesting this but...
Have you ever heard of Hot Shot No-Pest Strips? I once had a snake that got mites. The only suggested way to get rid of them was to pick them off one by one with tweezers. Can you begin to imagine trying to do that with a 12', 70# boa constrictor? Than someone suggested a Shell No-Pest Strip (Shell doesn't make them anymore, but Hot Shots are the same thing) outside her enclosure. I tried it and, sure enough about 3 days later she had no mites. We took the strip away, and she seemed to suffer no ill effects.
WARNING!!! Do not use them in an enclosed, poorly ventilated space. They are a vapor product. Remove them immediately once your mite problem is solved.
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Ivomec Exprinex. Zero withdrawl time so you don't have to toss the eggs. .25 cc for bantams, .50 cc for standards. Put it on the skin on the base of their neck.
Or Permethrin 10% spray. Spray all over the bird (under wings, vent, legs/etc) also spray down coop, roots, run.