IMO, processed carbs like bread, cheetos, fritos, doritoes, etc., are totally different from carbs that come from nature. I wouldn't restrict his overall carb intake, just make fruits and veggies (including rice, potatoes, and sweet potatoes) readily availble to him while making the "itos" food group something he has to buy with whatever pocket money or allowance you let him to have.
Almost any omelette you can make in a pan on the stove top, you can pre-make by baking it. Frozen pre-baked eggs defrost really quickly, so if you bake eggs ahead of time, especially in a muffin tin, you can defrost them when you get up and then a quick pop into the microwave to heat them when he wakes up.
I also wouldn't worry about how many eggs he's eating overall. They're a nice little protein with plenty of fat to feed his growing body and brain. Let him listen to his body for awhile without all the noise from the experts. He could very well change and adapt as his body changes - he might even grow up to be one of those healthy people who only eats when he's hungry and never has to worry about his weight.
"Right is right, even if no one is doing it; wrong is wrong, even if everyone is doing it." - St. Augustine