Does the egg aversion also include crustless quiche/frittata type options? I usually do an Asian type quiche where the dairy is substituted with broth. I also use firmer veggies such as pre-cooked potatoes, spinach, corn and broccoli so they don't fall apart as easily without the help of any cheese to bind. It's similar to the egg pucks that they have in Starbucks but without the dairy. Most of the time I just chop up dinner leftovers, maybe add more spinach, top with the egg-broth mixture and then put them all in a medium oven-proof dish and either steam in a pressure cooker or bake in the oven. Then slice into small bite-sized squares or use a muffin pan if you prefer the round shape.
For dairy-free, gluten-free options I find it easier to think of dinner for breakfast instead of traditional breakfast items. For example, rice balls filled with homemade breadcrumb-free meatballs, or potato balls/patties filled with the same.
I eat egg whites, but don't care for regular eggs generally. I'm fine with a crustless quiche or frittata, except for the heating up in the morning and the having to cook it the night before or weekend before.
Seriously, yogurt has been my breakfast for ages because I keep plastic spoons in one of my desk drawers, I don't need to heat it up, package it up, etc. I just grab it from the fridge at home, bring it in to work, and eat while I'm reading emails first thing in the morning.