I did exactly that a few times but I figured out a bit of a secret for that burnt ends is to get my oven rip roaring hot before I put the pizza in. Preheat the oven at least an hour at 450+ before even putting it in.
I don't have a pizza oven, just a regular kitchen version, but I've gotten my pizza down to a science and getting the oven super hot first has been the key.
When I make breakfast pizza, I just don't bake the eggs with the rest of the pizza. I make them separate and just put them on top after the pizza is baked so they don't get all rubbery.