It's an omelette....why would you use an egg ring?
Maybe you are using too large a pan for the amount you are making?

Yes, I confess to having egg rings, and they get used at least twice a week. You have to buy the right ones though, as they're not all created equal. We make a lot of home-made egg mcmuffins, and these are perfect for those.

I actually prefer the Amco, as the handles fold down flat which makes storing them easier.

Here's what I have:

Here is a link that might be useful: Amco egg rings

I make patties, about 3 to 4 inches in diameter. Four patties at a time in the electric skillet.
I'm not seeing very optimistic reviews on the egg rings though.

Well...you have to make sure the pan you're using is actually flat, (so the rings are flat) which is probably what part of people's trouble is with them. (There are a lot of warped pans out there, not to mention inexperienced cooks. Contrary to popular belief, not everyone knows how to cook eggs.) The pan also needs to be hot enough so the egg doesn't want to spread everywhere (but not too hot), AND I always oil or butter the ring before I use it. It's probably just a matter of knowing how to use it so it doesn't seem so fiddly. I wouldn't think of topping my English Muffin with just a regular old egg anymore, but then, that's me! I like the depth of the egg once it's cooked, and I think the ring keeps egg moist as long as your pan isn't too hot. It's all about the presentation you know!

Here's a bigger, four ring version. You may already have this.

Here is a link that might be useful: Norpro egg rings

I do use an egg ring, although I use it for sunny side up, which I think might be less runny than scrambled eggs.

I have read that adding milk makes fluffier eggs-- might work for egg foo young too? Or maybe separating, whipping the whites until they form peaks, and folding them back into the beaten yolks?

I used them sometimes, usually for sunny side up or for scrambled eggs to "fit" onto an English muffin for sandwiches. DH uses them far more than I do. I also have the ones that fold, and are nonstick. I think mine are RSVP brand.

I find you *must^ have the pan hot enough for the egg to set quickly in order to get the best outcome.

I don't have any egg rings, but I could see where they would be handy gadgets for making egg sandwiches and such.

Personally, tho, I prefer a "freeform" patty for my egg foo yung.

Linda