Oh right, I forgot about the whole legal system with pets.

Whoops.
I'll be honest, when you were thinking of giving two of your tiels up, I was thinking of offering to take them in temporarily and find them a home here, but that would still be risking the concequences.
English and american budgies are indeed the same, but from what I've heard, English budgies are a little more laid back, while american budgies are hyper, energetic, and curiously busy. So yours might get along with Coco if Coco is anything like Lucy.

And Brandon, where would the bird go? Most bird rescues and sanctuaries here in America are already overcrowded, and it's not like they can release them. I doubt the people in charge of that kind of thing actually care about the animals. I'm not saying it's ok, but sometimes, there is literally no other option.