OP,
Stop wordsmithing.
Bottom line is you need to improve your flying skills if you want a 121 career; how you do so is entirely up to you.
You may not have failed a checkride, but you failed to complete Initial training at not one but two 121 carriers. That will not reflect well on your abilities going forward, nor will refusal to own that reality and show 1. how you have remedied your deficiencies and 2. why the third time will be a charm for you successfully completing not only simulator training, but IOE flying the actual airplane.
Truth be told, if you want a professional flying career at this point you probably need to spend the money for a jet transition course AND first get some serious experience in a piston twin or turboprop.