I have similar experience in Europe. TRI/TRE with 14000 hours. So as I understand it is required a “special” or “ above average” experience in order to apply NIW program. If you are successful than the airline require you to fly from the right seat (which for you do not need the previous mentioned experience), because you do not have Part 121 experience.
I guess than to apply for a PIC position you should do it according company procedure/pilot union procedure, so end of the waiting list.
Or am I wrong?