Careful on that 737 type rating. UPS grilled me on that during my interview.
Makes it look like SWA is your #1 choice. Not sure about the other airlines. (If SWA is your #1 choice, then the choice is easier). Much easier to explain that the GI bill paid for it, but wasn't my case).
No need to study for that FEX written, go to www.allatps.com. No studying, just walk in, watch their computer program and take it that day.