I transitioned over from AirTran last year, at about this time.
During my 47 days in Dallas, we had a couple of newhire classes begin. Being sociable pilots who smelled free beer, we stopped by both of the Class Parties (these are held the night before the first day of class, hosted by the preceding class).
Both classes had a good mix of civilian/military. A number of guys had strictly corporate jet backgrounds. One was flying a Piaggio (turboprop). Looks like you are plenty qualified.
Best of luck, hope to see you on-line.