If you currently have a job and are able to wait, I'd do the company that you really want to work for, ASA. Something to think about, but your work history is part of your background (just like your logbook) and will be scrutinized in the future. What if one day, you are in a UPS interview and are asked about your 6 weeks with TSA... "Why did you leave right after they spent all that training money on you? Would you do that to us also if FedEx called you and asked you to start 6 weeks after we trained you?" That's not a line of questioning that I'd want to open myself up to. Just something to think about. Good luck in whatever you decide.