I would FEDEX them a copy of your resume with a cover letter saying you want to work there and follow it up with talking with them at a job fair. Not sure if they would be willing to bend on that requirement but showing interest in working there can't hurt.
As for the domiciles, they let you pick which one you want to be based out of. You will get your first choice. The aircraft are not based there. They airline you to the airplane on day one and home on day 7.