Had lunch with a 17 yr. SWA captain yesterday.
You will need well above stated mins. even to get interviewed. About half the classes are military. Varies. Civilian new hires have 5000-6000 PIC Jet. There probably are exceptions. Even with that, it's no guarantee you'll get hired, or even interviewed. Kind of a crapshoot. The competitive mins will probably change over time. They always do.
I have another friend flying in China. Ex-Aloha has maybe 10,000 hours PIC in B737s. Two interviews in the last 2-3 years. NOT hired.
It's numbers first, then what/who you know second with some luck thrown in.