Eliezer state elsewhere that he 3h 41m where the time the physical process needed - so they blew up the planet as fast as they could. (A hint is that ships are still evacuating when the process in the stars start and none pushes a button after the time limit ). But your analysis still holds, but the the decision in the story is not to blow up at half time, rather as early as possible.
Hoping to find more epiphanies?
So I hereby declare Berlin the Official City of European LessWrong community due to its unbroken track records of hosting this event.