Bull ****.
The training failures to date are primary training failures, and moving forward, nobody gives a hoot where the applicant got his primary training. His training failures will be reportable and part of the pilot record database for life, nor will they be the determining and ranking criteria in later job selection, if the original poster establishes a history of work and checking/training events that demonstrate having learned and moved on.
Comments thus far are germain and applicable. The poster presently has an immediate history of problem training and checking. This is damaging. It does not need to remain that way. On a level playing field, it will always be a potential discriminator, but with an adequate employment history that includes successful training and checking events, these primary training failures will fade and become minor. Presently this is a possibility only, incumbent on the original poster to get employed, and to ensure no further training failures occur. These events are not a career killer, regardless of changes in the hiring cycle.
Hiring comes and goes; several airlines that stated they weren't hiring in the upcoming months or year, have been regularly hiring. Airlines are far from the only source of employment, and at the experience level of the original poster, the field is wide open for consideration. Be a successful flight instructor. Be a successful 135 pilot. Tow some banners. Throw some jumpers. Chase powerlines. Fly the Grand Canyon. Air ambulance. Freight. Apply everywhere, and where ever one lands, exercise the study and work habits to ensure training and checking failures do not occur. Built a successful employment history.
One cannot do that without understanding where one is, and where one has been, and the reasons, and what takes to overcome or change those reasons.
Elementary, really.