From personal experiance, I cooked on a flat top with six 8" pans for two to three eggs and three 7" pans for single egg orders. I had one frying pan with an insert for poached egg orders. Avoid electric grills, gas is much better, but a steam griddle like the AccuTemp is best as they hold a uniform temperature much better. Use an IR thermometer to make certain the surface of the grill is 325º to 335º uniformly over the surface. Take the temperature on 8" centers.
Preheat the pans on the grill, take the bottom pan for each order, add the oil, we used a mix of half butter and half bacon fat, then carefully break the eggs into a shallow bowl and gently add them to the pan. Cook to order. I would often have 4-6 orders working at once. One important item: learn to flip the eggs, a hasty spatula will break yolks.
DO NOT set precooked eggs on a buffet. Set up an egg station with 2-3 cassette stoves next to the serving line and have a Petit déjeuner Chef cook to order. Set up a dozen fillings for the scramble and omelet orders, fewer will be disappointing to the customer, but more and they take too much time deciding.
For omelets and scrambles we would break and whip ahead 15-30 eggs depending on the time of day into a gallon cup. For one egg we would measure two and a half ounces of prewhipped egg, for two eggs - five ounces, and for three eggs - eight ounces. The left over prewhipped eggs would be set aside at the end of each hour for the use of the bakery. All omelets and scrambled eggs were made as ordered.
For most days we would use a skillet with a poaching insert due to the low demand. Sometimes we would have two in use. On Sundays we had Eggs Benedict on the menu as a special, and with the high demand in the morning we would use a large poaching frame in a steamer to keep enough being made.
Incidentally my skill level is Certified Master Chef.