the eggs had more water added than I realized
Uh what? If that number is anything other than zero I'm pretty sure you're doing it wrong.
I make perfect French omelettes nearly every day, and it's a 90 second start to finish process once the pan is heated. Other than whisking there are no required tools. Folding and flipping are done with the pan and a little wrist movement.
Unless your pepper is enormous (ex: cracked instead of ground) the size doesn't matter. Paprika is a garnish in this dish, and even if it were an ingredient its moisture content is irrelevant.
Getting the heat right can be tricky at first, until you figure out your equipment. I can't help but feel you're overthinking this whole thing (or trolling)