M.P.
First, with eczema, no creams or oils. These just aggravate eczema. It's not dry skin, it's an allergic reaction. Do plain, soapless baths and no creams. I only used hydrocortizone ointment on my son's flareup spots, and that seemed to help.
Another big help is to cut out all fragrances or dyes. This means free and clear detergents, dryer sheets, baby shampoos, etc. All those fragrances and dyes compound the problem. He may not be allergic to dyes and fragrances, but they make the itching worse during a flare-up.
Also, you didn't mention nuts. Are you also eliminating all nut products or foods processed at plants that also process nuts? That's a big one to cut out. My son had nut allergies, and me eating nuts would throw his eczema into a frenzy.
Finally, make sure you keep those fingernails as short as possible. This will minimize any scratching that breaks the skin.
The most important part is to keep the eczema flareups contained. Sleep will be so much easier to tackle once eczema isn't ruling the roost.
Hope this helps!