A very late update from us... After FS and then partial FS we had to limit our diet more and more, till we were on 1 fruit, 5 veg, meat and bread. And he was still reacting.
Since then we started biomedical treatment (thanks to Erin who told me about the Facebook group!) and found Jake had low zinc, high copper, vit D deficiency, 2 parasites, high yeast and pathogenic bacteria in his gut! All of those cause food intolerances and eczema.
We started supplementing him and went on a Paleo/GAPS diet to heal his gut, kill the yeast and bacteria, get rid of the eczema, and get rid of the intolerances.
We have now managed to get to a point were we can eat all veggies (though we still avoid nightshades which are linked to eczema and other autoimmune issues), fish and meat! We are limiting fruit as much as we can as the sugar in fruit feeds the bad bacteria and yeast, and we're trying to starve and kill both.
If anyone is interested to see what a paleo/gaps diet is like and get meal ideas, check my Facebook page: www.facebook.com/AutoimmuneAndLeakyGutPaleo