With the amount of hiring projected in the next 10 years, the only downside to stopping your application/interview process halfway through would be the incredible seniority (lifetime earnings/quality of life) hit you would take by postponing your airline career.

AA, DL, SWA, UA, FedEx, UPS will be desperate for military pilots going forward, so little things that would normally scuttle prospects of being hired at a major today (like turning down a job) will matter less/none in the future.

Only you know all of your circumstances, but are you familiar with USERRA and have you checked into the Air Guard and/or AF/Naval reserves?

Start applying now.

Good luck.