I would not treat the chicks until they are grown. But I would try to get some of the adult’s feathers looked at by a vet for the feather mites in the feather shafts to really get a diagnosis. Are you seeing sores or skin damage? Do you know anyone with a microscope to look for the tiny mites? If it is just bare skin, and the feathers don’t grow back until after a molt, I still think it could be feather picking. Do your birds use a dust bath? Have you done a deep cleaning of your coop after treating them with permethrin? I have never seen feather mites before in my chickens. Here is some reading that may help.
https://www.merckvetmanual.com/poultry/ectoparasites/mites-of-poultry
https://poultrydvm.com/condition/depluming-mites
Thanks for the resources! It's always helpful to read more!
I don't have a vet or friend who can look with a microscope
I've dealt with common times of mite and lice before and can't find any visible signs of them, so
if it is a mite it's not Red or Northern Fowl. That much I'm 99.5% sure of.
I treated the birds with permethrin dust three times and saw no improvement. A few birds continued to get worse during treatment. Everything I read, though it wasn't mentioned in these two sources, said that liquid (whether it be ivermectin, permethrin, etc.) and sulfer is the only thing that had effect against depluming mites.
I have given the coop a thorough clean and sprayed with a homemade solution. I sprinkled elemental sulfer everywhere but it is small flakes, not dust, so I'm not sure if it's doing anything. I'm using that in the chick coop bedding too.
The specific symptoms I've been seeing, roughly in order, are 1) loss of feathers (first under the wings and at the base of the tail, then the front of the neck), 2) dry, red skin, and 3) a couple hens got to the point of slight bleeding at the base of the tail. Except for one hen who showed signs last fall, signs appeared on my birds when the weather warmed up. When I treated with ivermectin all bleeding stopped and the skin turned a bit closer to normal. The feather loss seems to have stopped too (though it's hard to keep track).
They have dirt to dustbathe, but no specific spot (it seems different every day, unlike previous flocks I've had) so my wood ash and sulfer might not be taking affect. I'm considering making them a bath in a tub.
As for feather picking, I haven't dealt with it much before, maybe because my previous flocks were better behaved.

Does it normally make the skin look red and irritated? Where do they normally pick feathers from?
I think I'll make them a couple homemade flock blocks just to be safe.