Not sure how fighter time is actually "crunched" but whatever you have will more than likely be enough. Since all of your time since day 1 is PIC, you'll have no problem with that particular requirement. FDX is full of ex-military guys, with probably more fighter types than heavy types. Your major obstacle is not your flying requirements, is the three internal recs, with a couple guys who've flown with you included and a sponsor. Fedex is hiring like gangbusters right now and rumors indicate that it will continue. I'd start planning as early out as possible. Get your ATP, your FAA Medical, your RTO license, and your online recommendation to fedex (
www.pilot.fedex.com) ASAP and start calling your buddies who work there - out of the blue if you have to. Would also be a good idea to be thinking about where you want to live and commute to/from and whether or not you want a guard/reserve job thrown also (highly recommended, especially the first year). Ideally, you want to have a job that starts when your terminal leave begins. Fedex will want to know your availability date up front. You can do your meet and greet with the ACP anytime, but probably won't get an interview until no earlier than 2 months or so from your projected availability date.
Not sure about SWA or UPS stuff, but I'm sure someone will answer shortly. There's also some good threads on the "other" forum, flightinfo.com