My scalp psoriasis was horrible. I would use Dovonex and betamethasone and then they came out with Taclonex which is a combo of both. It helped the most out of all of the topical meds. It’s a one to be careful with though. Overuse of topical steroids can cause skin atrophy. The best medication was Humira. The plaques started to come off in a few weeks. After a month, I just had redness on my scalp. No inching or plaques left. After a year, I have one tiny pencil eraser sized spot on my elbow that is persistent and won’t go away, but that’s it. I didn’t realize how much psoriasis bothered me until it was gone. It is so nice to wear dark colored shirts without worrying about flakes. I was also able to get a cute, short haircut that is more manageable now that I have PsA. And, when my hair was long, I was finally able to wear it up without worrying about my plaques showing.
The home remedies, are ones I’m sure that you have tried already: coal tar, salicytic acid, sun, tea tree shampoos, or straight tea tree oils. The only thing that really worked for me were the prescription meds though.
I’m so sorry to not be more help than that.