Bonger:
There is no list. They have an avoidance bidding system.
When First Officers bid for their monthly schedules they can enter three seniority numbers they do not wish to be paired with. Should the bid result in being paired with one of the three numbers it skips that schedule and moves to the next choice.
The seniority numbers of captains First Officers wish to avoid are not published by the company.
Sounds like a list to me, published or otherwise.
Conjecture:
Having been an airline management-type (with a seniority number) in the past, the company is well aware of her status among the other crewmembers. If she was indeed fired, that record, along with this LGA accident being the final straw, was enough to justify termination of a female captain. Believe me, the company doesn't want a pain-in-the-a$$ crewmember around anymore than the majority of FO's, particularly a company with the operating philosophy that exists within Southwest.
Now, the union has to decide how it will proceed in "protecting" one of it's members.
End of conjecture.
Be interesting to hear the crew interaction during the final moments of the flight.