j.nips,
Just my humble opinion, but I think the factors you mention above have been an issue in the past...and may be in the future. In the current environment, most of them aren't as big an obstacle as one might imagine.
This current hiring binge will come to an end some day and those factors may come into play again. My guess is that a green card won't be a negative (for well qualified pilots) even when hiring slows down.
In the meantime, if someone wants to fly here, apply to every place you might even remotely consider working and see what happens. They can't kill ya and eat ya for applying.