Morrus said:I'm also unclear on the relevance of the timing anyway; what difference would it have made when it happened, other than last-minute dramatic timing?
The relevance is that everyone on Earth had to be thinking about the Doctor at the same time. And if (big if, since I don't recall seeing anything to confirm this) the Master's countdown was being seen around the world, that might have been the only way to achieve the kind of synchronicity needed to make it work.