I'm guessing you guys have been pm'ing, hope that things are improving.
I would make that derm appt, in case you're still sinking around with this then, since you can always cancel it, and I would definitely do a thyroid trial, I think that's really important.
You night try daily baths for a week and see if it makes a difference. I had all sorts of special shampoos and stilll found this one to be the best:
https://www.chewy.com/vets-best-hot-...-dogs/dp/45180 When my girl had that black it was a resistant staph infection, luckily she responded to clindamycin, as I don't like using the cephalosporins.
I also treated for thyroid. Your vet needs to step up on this.