First off congrats to the OP for persevering. Going through indoc, sims and all that stuff at two different companies, and making it happen is something you should be proud of. If anything shows you are dedicated. Get some flight time and successful recurrent training behind you and no major airline is going to care about the initial failure.
To be fair, other airlines might use slightly different terminology than mine, so you could be right. At my shop, your type rating is issued based on completion of systems test/oral + MV check sim + LOE check sim. LOE being the final check event before you go out the door for OE in the aircraft. I never actually cared enough to get a straight answer, but I believe all 3 of those events are considered to be "jeopardy" events in the AQP system.
As far as I know all AQP systems operate in a similar manner. The critical events are your KV (knowledge validation) MV (maneuvers validation) and LOE (line operations evaluation?) Prior to KV you have a few weeks of ground school and some tests, including a mock KV. MV and LOE comes at the end of simulator training.
I went through this process at a regional not too long ago and I was surprised at the number of people who had trouble with LOE. On paper, the MV is the hard one, its an hour and a half of approaches, landings, engine failures, V1 cuts, single engine ILS with a single engine missed approach. The LOE should be easier, its a routine flight from point A to point B with some average adverse weather.
If I had to venture a guess as to why the LOE was so difficult for some, I think it is because the training departments focus the sim time heavily in favor of the MV work, since those hand flying skills can't be developed with flashcards or a paper tiger. The LOE is focused on checklists, flows, limitations, procedures, briefings etc... it takes a lot of focused self-study to get proficient at that outside of the simulator time they give you.
LOE is the final checkride before you go out to fly the airplane on revenue flights on IOE (initial operating experience). With AQP the training and checkrides are the same for an ATP with 5000 hours in type or a 1500 hour flight instructor from riddle. I happened to take my LOE with the director of the training department who rarely gives checkrides. When we finished he casually asked me to confirm if I needed an ATP and Type rating.. I thought it was kind of a funny question "well if you're just handing them out, sure!"