I'm glad you are going to be taking care of them!
You are on the right track with using the Permethrin dust on the hens. Repeat the dusting in 7 day intervals.
I know you cleaned out the coop, but did you also treat it with Permethrin? If not, then using a Permethrin spray is a good idea. Why spray? You can purchase Permethrin concentrate which is more economical, spray is much easier to apply to housing since you can get it into the corners, nooks/crannies. I do prefer spray for housing, dust for treating birds, so I keep both forms. (Repeat spraying the coop/housing in 7 day intervals too)
The skin issue is probably from the lice, a little picking/scratching at herself and maybe nutrition.
Again, you are on the right track with the feed. You've have excellent results with vaseline with your other hens, so you can try a thin coating on there to help sooth that or if you have hen healer try that.
How do their legs look?
Follow Carol's (azygous) article on treating the crop. I know you got this!
I look forward to your updates.