it is hard to cook a simple omelette on an electric range: you need a very hot plate to go down to a simmer very fast -

"Simmer"??? what are you doing to those eggs? Plain omelette should take 30 to 45 seconds on high heat if cooking on an electric burner from butter in to eggs out, no change in temp. req'd, then onto a heated plate and serve. If you Simmer you are on the road to chewiness, a bad place to go in this case :-(

Never more than 3 eggs, if you need more than that make another omelette.

http://www.youtube.com/watch?v=GpIndUafTJU

What CAN'T you learn on TOD?

your description is much better than mine, but essentially it is the same process.
I heat the pan with oil or butter on a big flame, throw in the lightly beaten eggs, turn the heat very low, sculpt the omelette, season and serve within a minute of the eggs having hit the pan. Yum!