Corn is another big eczema trigger, so don't try to replace gluten with corn (corn tortillas, etc.). If the eczema is not caused by an IgE allergy, the most common causes are dairy, gluten, soy, corn, egg. So be careful subbing other things.
3 out of 5 of my family are dairy, gluten, soy, corn free (and one is egg free besides) and free of a lot of other foods, we're not by any means going hungry.
Breakfast: fruit smoothie (coconut milk yogurt or coconut milk, banana, frozen strawberries, pineapple juice), bacon or breakfast sausage (yesterday it was gluten-free donut holes) or millet porridge made with coconut milk, or hot buckwheat cereal with cinnamon sugar (can add dried fruit and chopped nuts to it as well)
Lunch: leftovers
Dinner: chicken mirabella over rice, black beans and rice, zucchini-chickpea fritters, stew, roast chicken with gravy and rice, roasted veggies, we make gluten-free/dairy-free pizza with a buckwheat crust, pot roast with gravy over sweet potatoes, taco salad, chicken marsala, butternut squash soup, rice pasta with meatsauce, fried rice, stir fried veggies over rice, there are so many options!!
I agree: increase proteins/fats to feel full. But good fats not processed fats.