Going primal/paleo really has not impacted my psoriasis much at all, sorry. I have had it for 36 years. For scalp plaque I have found a great shampoo though. I use a brand called Joico. They have a shampoo called "treatment" shampoo. (it used to be called "bijoba") After about 3 weeks of using it I noticed a dramatic decrease in flakes and redness.
granted, I have not yet tried the "autoimmune" protocols suggested by Robb Wolf for addressing AI issues (Psoriasis in an autoimmune disease). For that I would need to give up eggs and I love them too much. He also says you should drop all nightshades from your diet as well for AI issues. For now my psoriasis is in check and managable without any medication, just lots of lubriderm lotion.