I've interviewed and been rejected by SWA twice. My Airways interview in December went well, and I was fortunate to get the job. I don't think anyone can think of themselves as over-qualified for any flying job right now. There just aren't that many places hiring, and the competition is still very fierce.
I don't know the qualifications of the others who will be joining me at Airways, but as for me... nearly 10K hours, 6500 PIC, three type-ratings, check-airman, no training failures, degree, clean record, good recommendations, currently work for a wholly-owned.
So that's who you're competing with, and the bar will remain high for a long time to come. Remember, the "pilot shortage" has not yet begun, so brush yourself off and work on becoming more competitive. Believe me, I know what rejection feels like. It's a tough business, and not everyone will get a job at their first-choice carrier.