Second the above comments about the GC situation. Most companies get "jittery" unless you show right to work and some won't hire unless you have the fully paid up GC (Permanant Residency) in hand.
In addition to FedEx (I'm flying for one of their feeder companies), Southwest have been known to like ex-Military guys. On the freight side, you might also want to try Ameristar or Cherry Air (Lears & Falcon bizjets). When push comes to shove, the best credentials appear to be multi-crew PIC time (known as pt 121 or 135 time in the USA).
Good luck