I never really got the Bran = NK theory - but
having watched this video (3:00) I have to say it makes as good a story as anything else.
I would make it go something like this
1) Bran cannot see into the future, past the Battle of Winterfell. Therefore he thinks they are going to lose the battle.
2) In desperation, Bran wargs back to when the Night King is created to try and stop that from happening. (But the Ink is dry)
In fact he wargs into the human that becomes the Night King himself
3) Exhausted from Warging so far, he can't wake up/warg back.
4) He begs those weird half creatures not to create him but they gag him and do it anyway
5) Warging Bran becomes the Night King
6+)
Current day Bran is stuck warging into the past and can't wake up. This is why the Night King is so drawn to Bran. This is why the Night King has the same abilities as Bran. The Night King doesn't want to kill Bran at all, he's waited thousands of years to take him.
Then you could have had a really creepy moment where John kills the Night King, but none of the dead are destroyed. Instead, Bran (still with eyes rolled back in Warg form) stands up and walks towards Arya. He opens his eyes and they are bright blue like the NK. Then Arya has to kill Bran and finally the undead are defeated.