Can you give an example of an egg replacement recipe? I don't eat eggs but sometimes egg replacement in recipes I see is for something like flax seeds with water but depends on the recipe.
Egg yolks are higher calorie and fat than egg whites which is why you see a lot of diet recipes call for egg whites. In some recipes, egg whites are used for lift (soufflé type recipes).
For egg yolks, you could feed them to your dog if you have dogs. You could mix them in with a salad or a breakfast burrito or whatever else.
You can't out-exercise poor eating habits.