I know you say you want to avoid moisturing, but its part of the recommended treatment/prevention program. If you don't want to, and you are doing basically everything else there is to do, then I would suggest using a hydrocortisone cream on the patches immediately. It helps the skin retain its own moisture content and can be weakened if you wish by applying with a little moisturiser. I have found dermaveen or aveeno to be the best in the way of moisturisers.

Think about joining the Eczema Association, they send you all the latest information and samples about once a year, and you can always contact them for advice.Eczema Association of Australasia Inc