This may be redundant but I think it may be applicable. Many years ago I aquired my commercial through the military competency test. I later went and got an ATP while flying commuters. While flying as a full time civilian pilot I received a checkout in the CH 47. I took my certificate of completion to the local GADO and he issued a BV-234 type rating on my commercial certificate. I had several type ratings on my ATP at that time but the only way you could get an ATP type rating was to get a Fed who was in the Guard/Reserves to administer the check ride and he, obviously, had to be a military IP as well. I believe the highest certificate/rating available from a strictly military environment is at the commercial level. I can in no way speak for SWA but I believe they want a 737 ATP type rating.