How do I keep eggs from sticking to a pan while cooking?
This combination is never going to work - it will stick no matter what. 

If you want to keep this method of baking, you will have to switch the pan. A nonstick pan will work, and while it is new, you might even be able to slide off the eggs without any crust sticking to the pan (while later it will be just easier to clean from the stuck stuff). You might also decide to switch to a glass pan - it will also stick, but you will have an easier time cleaning it, especially with a bit of a soak. Using glass in a toaster oven will make the eggs stick a bit more though, because it creates a stronger crust. 

In both cases, there will be some time involved in cleaning that's more than just cleaning, say, a bowl in which you reheated some soup - there is no way around that with your chosen method of preparation.