When it comes to Kirk's promotion, I say just embrace the mythos. Kirk's quick rise is the stuff of legend.
If you need another reason to justify it, consider this. Starfleet just lost seven starships with seven commanding officers. Vulcan is gone and the larger part of their fleet is in some system apparently engaged with another enemy. You have Klingons, Romulans, and maybe Cardassians at the gates. Kirk was incredibly successful in stopping an advanced enemy from saving the Earth. Like someone said, you don't give him a mop and have him start at the bottom. He's earned his shot at the top seat.