This may help:
Go to Allegiant, Frontier, Atlas, ABX, Kalitta, JetBlue, Spirit, Vision, or some other carrier with a larger and/or Boeing/Airbus aircraft. I think that this DOES help pilots go to the "Big 5". I am at Atlas, and have seen a lot of guys go from here to the "Big 5". We had one guy here who had 3 class dates: AA, UAL, DAL. Another guy, from here, finished INDOC at UAL, and two days later resigned for class at DAL. We have had a LOT of guys to to FedEx, and now a lot going to UPS...apparently 120 or so of our pilots in the UPS pool, minus the pilots who already left in Jan.

I am not saying that this is THE way to go, just offering a suggestion. Some years ago, I had all the requirements for a large PAX carrier, but they said I needed glass Boeing or Airbus time to be seriously considered.

Of course, the longer you wait, the worse the Pilot Shortage gets, and the easier it gets to go to the Big 5.

PS-Maybe Amazon will make it the Big 6...