For what it's worth, I had a similar experience trying a strict AIP diet for a few months - some improvements in my autoimmune symptoms (some psorasis I've had since childhood), but nothing definitive. When I tried a strict carnviore diet, basically cutting out the vegetable and fruits allowed on AIP, my existing patches of psoriasis disappeared over a few weeks, and no new ones appeared.

Since then I've gone on and off of strict carnivore, but anytime I reintroduce vegetables and/or some other carb sources, I'll start to see new patches of psoriasis pop back up within a 2 or 3 weeks usually. So I usually balance on that line now, returning to carnivore if my symptoms start to bother me too much.