The notion that there is some perfect pedigree, some perfect CV that most applicants to the NIH (or other funding body, I assume) possess is untrue.
Oh, it can be comforting, I realize. To think that if you only had picked the right doctoral or post doc lab, if only you had been able to move across the country, if only that damn PI had written you a better letter and gotten you that job at HighFalutinU....
But for those slings and arrows of outrageous fortune, you too would get every application funded. Nary a triage and seldom a revision.
Many, many funded PI's of my acquaintance have holes in their CVs that you can drive the ParanoidApplicantTrain through. The wrong doctoral Uni/program. Dismal productivity in a crucial stop. No post doc. Too many postdoc years. A less-than appointment. Seeming lack of independence. A mid career research drought. Low IF pubs. A scientific diversion. Too narrow a scientific focus. Too diffuse.
The thing is...the extramural, NIH-funded community is diverse on this axis. It permits a lot of room for Investigators who differ from the "ideal". To the degree that the "ideal" is more of a fantasy of the unsuccessful applicant than it is a reality.
My charge to you is this: Ignore your seeming deficits.
Ignore the inner voice telling you that easy street was back there on the path not taken. Or the path that was barred to you.
Focus instead on crafting the story of you, as a scientist and investigator. How did your experiences make you the independent scientist that you are?
Remember that you are not talking to your detractors but rather to your advocates.