You can eat the eggs after you worm them. There may be a withdrawal period, where you'll want to discard the eggs, but that's only a few days, I believe. Pick up a bottle of Valbazen liquid goat/cattle wormer from the feed store when you're there next time.

It's a little pricy, but it lasts forever.
I have no experience with permethrin... We always use Sevin dust around the coop and add it to the places where they dust bathe.

Maybe add a little permethrin to their favorite spots?
Unknown about the coconut oil... You could always offer some on a little plate and see if they fight each other for it. That would be a good indication.
In the meantime, I would cover the bare spots with some iodine. That will hide any red, irritated skin, provide a little bacterial protection, and discourage other hens from pecking at exposed tissue while we figure this out. <3
MrsB