Which makes me think the NK might detour Winterfell, burn down the Citadel then head east and level King's Landing while what's left of the northern army retreats south.

Remember when Sam checked in the guy told him that these books contain the entire history of man. Maybe NK goes there to destroy that first and then comes back for Bran. I dont think he goes to Kings Landing. He has to die at Winterfell. I still think there is something to do with the dagger Arya has that she got from Bran. I also think they foreshadowed it in E2 when she was throwing those daggers in front of Gendry.
I also think Melisandre has to show back up at some point in the battle too. Part of the endgame might be her having to burn the weir wood tree to keep the NK dead?

Is due to Dany's vision in the house of the undying that shows her the throne room, without a roof, and snow falling in it. And the dragon flying over KL that Bran sees in a vision.