I would send out the may day (urgent) once the list has developed - list means taking on water or your bouyancy is otherwise compromised. 2,000 people aren't worth screwing around to see if it works itself out.
I wouldn't order abandon ship yet, but I would order everyone into life jackets and survival gear and to stand by life boats. Hopefully after two hours another ship will be on station to take on the passangers, but once it becomes obvious that she's going down, we must abandon.
I'd be the last man off but not go down, that's just silly and fantastical.
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