I hope RPD helps.
I don't have eczema or psoriasis, but RPD helped reduce my scalp and eyebrow flaking a little bit. RF honey helps a bit more, but only temporarily. Clay seems to help a bit, but again only temporarily. About half-way through my bottle of Primal Defense Ultra, which has L. Plantarum in it, I seem to be having significantly less flaking. Time will tell. Prescript Assist, which doesn't have L. Plantarum, didn't help at all. One of the Heisenbug success story people took Jarrow Ideal Bowel Support, which I haven't tried yet. It sounds like even the people with good results from probiotics tend to have to continue taking them at least intermittently.
Down the road there is medical fecal transplants, which I'll be keeping an eye out for, that reportedly help with many chronic issues.