Get flying immediately, and don't wait to apply. Even if SWA would hypothetically hire you non-current, it could be months before you get a call. Spend those months flying and when you get to the interview, you won't be non-current after all.
Get any flying gig asap, and then just keep updating your application every couple of weeks. At some point your app will trigger an interview and whether it's sooner or later, you're better off showing up already in a flying job.
Get those 135 hours and apply to your dream jobs plus whatever regionals would work best for you (living in base, etc). A lot of military guys spend just a few months at a regional getting some hours and 121 experience while waiting for an interview at a major or legacy, and it undoubtedly helps them out.
I got hired by spirit with only my ATP course in the previous 5 years, and a year later SWA offered me an interview. That's a fairly extreme example and I don't think spirit is doing that sort of thing right now but almost any regional would be happy to get you onboard while you're waiting. Skywest is very popular with mil pilots who need recency or some more time to be competitive.
Also... The "actively flying for 2 years" is desired, not necessarily required. I didn't really have it and didn't try to disguise that fact. At the time of my SWA interview I had about 14 months flying for Spirit and nothing but my ATP course for the 4 years before that. Although my logbook reviewer raised his eyebrows a bit when I confirmed the zeros in my recency summary for previous flying over the last 5 years, he never actually brought it up in our discussion other than confirming that the timeline and summaries were correct.