Crew should have put themselves in "time-out" as soon as they stopped at the first airport - and I wouldn't want to fly with anyone who thinks otherwise. Other than that, I have no comment on discipline and regulatory response, until the facts are better known.
Exactly. If I ever found myself in this situation, I would fess up then await instructions. Trying to “make it better”, although instinctive and laudable, does not go down well with flight management these days.
Don’t dig yourself deeper into the mire. Put the park brake on and go off duty.