Another pilot, another solution.

I concur with the notion of getting some turbine PIC time and ATP hours as quickly as possible if you want to go to a major. The right Part 135 job could do that. But rather than thinking of the majors as the ultimate goal, why not think fractional? Two years at a regional will get you to 2500 total time and a great shot with NetJets or FlexJet. Great QOL, reasonable upgrade times, chance to make $150K a year before retirement. They like military experience - but the real emphasis is on customer service experience. So try to get a flying job that gets you some face time with passengers.

Good luck.

Go Navy, Beat Army.