What an oily mess! :o)
I do not have a clinical solution. I do know that my son used to develop rashes and soars from standard bar soap. I then started selling Mia Bella's Gourmet candles and body products and in that line there is a soy and tea exract soap that he started using. He has no had a rash in two 1/2 years when using that soap. It is very gentle on the skin. It also last a very long time.
I would not have "solicited" you like this if you had not mentioned the exzima issue. I just know how much it helped my son so I thought I'd pass it on. You can check them out at www.IwantAMiaBella.com. I have a number of bars on hand if you decide you would like to try one.
People use this soap on their dogs with dry, itchy skin. Men use it on their hair and women who do not color their hair. We have one in all three of our bathrooms as it really helps with this dry mountain air. It is a wonderful soap that comes in 5 different scents; Sweet Orange & Chili Pepper, Slate & Stone, Mystic Melon, Grapefruit & Lavendar and Juniper Breeze.
Hollar if you want to give them a try.
Blessings in this oily journey! :o)