I think the only real way it would turn out with Bran as the Night King is if the Night King is being controlled by a future version of Bran and he's worging back in time like he did with Hodor.
I think the Night King, the Gods, etc are basically just a version of Bran. He was warned not to mess with events yet he yelled out to Ned at the Tower of Joy. There's also the theory that Bran made Aerys mad with his whispers and that kind of ties into it. He could of easily created multiple version of himself through his attempts to manipulate the past.
The show has dropped several hints that Jon Snow is actually the son of Rhaegar Targaryen and Lyanna Stark (which also happens in the book). If that's the case then Dany is Jon Snow's Aunt so it could be awkward... or maybe not.
I don't think it's a warg 'cause that would mean that the King had to warg one through secondary connections. Technically the King is the one that started it all so if you killed one then it shouldn't make a difference, but they killed one that raised a group and the group all fell.
I think it's more of a vampire thing. Kill the master and the lower ones all die. So it's like a network. The king passes his life force onto his subordinates to pass it on to others. If there's a break in the network then everything below that crumbles.
Jon being Rhaegar's son is pretty much confirmed now unless they're pulling the biggest troll ever. Sam and Gilly even have the book to say that he married another women and Jon isn't even a bastard. Only Bran in the show would know this though? Also it wouldn't be that awkward...most people would wanna fuck Dany even if she was their aunt haha. It's normal for her anyway.
Ahh so it's like the whole thing in The Strain with The Master basically controlling all the *****? Bran could try and hack into the network and hijack the signal like the Night King did with Bran and the Ravens.