What I am finding works better is to set the pan on medium heat, then add the beaten egg. I will then drop the heat level to low to finish cooking. This has been more successful at getting a uniform, pliable cooked egg layer to fold over to make the omelette, though I have not yet been able to get that slight degree of browning on the outside that I like to see in an omelette. Perhaps the efficiency of the ceramic nonstick coating prevents the browning. In any case, it has been a learning experience for someone who has been cooking omelettes for quite a few decades now.
I believe I shall enjoy these pans once I get comfortable with how I need to use them. They appear quite sturdy, and while they are a bit heavy, my hope is that they will last as long as the Calphalon pans did. The Caraway pans are rather pricey, but if they last 15 years, the per-year cost is quite small.
Those are my observations of the Caraway fry pans after a month and a half of use.