Type or no type
The good news is you're in a stack of names that will get interviewed. The bad news is you are in a large stack with folks who may have more or less experience than you have but you are competing with folks who HAVE types in the other stack.
Lots of variables will determine whether you wish to move from the large stack to the small stack i.e. affordability, available resources, time off, level of desire to work at SWA, etc. The important thing to remember is that while at some point SWA will open up applications again, the current requirement is that one MUST have a type to apply. In other words, everyone that applies from this point on (until SWA changes the requirement) will have a type when you don't. While I can't say definitively say they will be called before you it would make sense a "competiitive process" would tend to favor those who do have a type over those without one.
You have control over a lot of things to include improving your chances of getting called. Did we interview folks without types with folks who had types? Yes, you bet. We even hired many of those folks without types & they then had to get a type within 6 months. But that was then, things have changed dramatically. One reason why the requirement was put back in place. It is not an easy decision & one that each person must weigh in these difficult times. Good luck in your search for the best airline for you.