thank you for your answers - very helpful. now I just have to make some clarified butter.

If you were cooking at an omelet station at a breakfast buffet in a fancy hotel or resort you wouldn't be using a non-stick pan but a copper/stainless omelet pan (or at least I hope). You would have a something with a 1or 2 oz ladel full of clarified butter and you would get your pan hot put a ladel of carified butter in the hot pan and swirl it around to coat the surface area inside the pan and you would add your egg. You would be cooking on high heat and you would finish your omelet in just a minute or two with out browning any of the egg. Doing without fat is not something that I would do. But, I do remember a day before non stick. Just my two Bits! Good luck!

Use far more butter and oil than you'd think is needed for a non-stick pan. Like was said, it's tricky---depends on the pan, the temp of the pan, the temp of the eggs. Most omelet recipes call for non-stick and much less oil/butter than a steel pan.
I now prefer my stainless pan and a combo of clarified butter and olive oil.

I make lots of omelets, almost every day, all in a heavy stainless steel pan. I used to make them in a thin stainless pan, but the handle fell off and I got a wonderful Demeyere pan that can handle anything, from omelets to steaks. Sticking is no problem for me. But I am not afraid of a little butter. A couple of years ago, I switched to olive oil for a while, and they didn't stick either. If you're willing to accept some fat of some sort, my advice is simply to practice. Make a lot of omelets and get to know your pan.

That's gonna be tricky. Oil it really well, with melted butter preferably. Good luck!