Again FWIW.
I used permethrin spray on a day 1, 5, 14 cycle at the beginning of my efforts. I sprayed around their vents, under the wings, on their backs and chest each time; two people one to hold the other to spray, ensured that the spray was directly onto their skins. I also emptied the coop/nest/etc of bedding and then soaked the coop inside on floor, walls, ceiling. I still had mites.
Because winter started I had to switch to a powder insecticide. I am in Canada and was unable to get a powder form of permethrin so did some research and found 99.5% sulphur recommended so purchased a 50lb bag at my local feed store (cheap and does not build resistance). I dusted all the birds on a weekly basis and also mixed the sulphur into my dust baths. This regime has eliminated the mites so far... Note that sulphur is safe to use on a continued basis and I will keep using it my dust baths.
I cannot say that continued use of permethrin would not work, just that i could not spray the birds in below zero temperatures. I was also cognizant of the build resistance issue.
Keep up the fight, best of luck.