Every time I was involved with corporate flying, I learned to hate that part of the industry more and more. So, I can't really be objective in helping you make a choice. However I have a couple comments about the part 121 side of the house.
We're all on the cusp of some extraordinary hiring. There are questions about getting enough qualified pilots, or even enough people that want to become qualified. In reality, anyone who right now is anywhere near an airplane in any kind of flying capacity, has a pretty good shot at a major airline job in the not-too-distant future. The real question isn't whether you might or might not be cooked recruited by a major; the question actually is what is your seniority going to be? Where will you fit in the hiring bubble? As you've already discovered. Being hired near the end of a hiring push is bad.
Therefore, if I were you, and my decision was to try for a major, I would start with the premise that the clock is ticking. Second, I would take it as a given that I am definitely going to be a viable candidate. I would anticipate that requirements are going to shift, and they're going to shift quickly. Today's absolute minimums will become tomorrow's pipe dream. At some point I will become the most qualified candidate around. Therefore, the real challenge will be to be completely prepared BEFORE that point and be hired as soon as the environment shifts towards me. I wouldn't want to be the guy that waits until he's absolutely certain that he is competitive, before he puts his stuff in. At that point, he will have lost hundreds, even thousands, of seniority numbers.
So my advice is not to sell yourself short. I suppose it's always possible that you might be able to secure an interview in front of someone who feels you are not quite qualified enough. Maybe someone isn't going to like your PIC numbers. The good news is this: there will be many airlines hiring in your future. If one interview doesn't work out, move onto the next.
Good luck to you!