Recently you were asked to resign following a training failure as F/O; it was not a minor event. Presently you're reporting numerous rejections from various companies. You've never been a captain, and having just been rejected as an F/O applicant by Mesa, you're asking if you should reapply to be a captain?

Your recent descriptions of your situation reveal numerous deficiencies in basic airmanship; very large, glaring ones, as well as a clear failure to prepare for the training event that cost your job . You've indicated a strong sense of denial, have made light of the events and refused to own them, but instead of tried to explain them away or deflect or even project onto others. Your approach to the job, your attitude, and your elementary root flying skills are what you need to confront first, before you press on. You've showed a consistent willingness to blame others for your failures, and have minimized what are large, glaring errors that cost you your job. This is your landscape: put your house in order, figure yourself out first, before you go any further. With the most recent event, you were dismissed by unanimous decision of the training review board, and even your union representatives' response was to try to find a place that would take you. The union did not try to support you. That all those around you see this and you don't, should be telling you something, and it isn't. That you'd be rejected for an FO application and in any way, consider reapplying as a captain shows a massive lapse judgement. STOP.

Your airmanship needs work. Your aeronautical decision making is questionable. You're not taking your job seriously, else you'd have taken the months that you had to prepare for this last training event and got ready, instead of showing up rusty, unprepared, and failing to exercise the most basic elements of airmanship. Seek training. Get evaluated and accept the evaluation and the training recommendations that are given. You're not able to see the problems for yourself, but you had better be willing to let someone show you, and to pay them to do it, or you're looking at a very short career. You need clear direction on what you're doing wrong, and you need to humble up and listen, and learn. In no way should you be this far into your flying and still be making such elemental errors in judgement, operation, and airmanship.

You need to seek interview counseling. You need to get evaluated by an interview professional who can break down in detail where you've been and how to not go there again. Whatever this costs, pay it. Don't scrimp.

Now, you did say you'll only discuss your training failure privately, but you've already spelled it out on this site and presently it's carrying across multiple forums as you're applying multiple places, and commenting on it (like here).

What you have going on, is fixable, but your comments so far do not suggest you're interested in fixing, but rather denying. Until you get past that, further progress isn't possible.