[b]Bran, Arya, The Butcher’s Boy:[/b]

At the end of the day, Bran still got pushed out of the tower and becomes a cripple, yeah? It’s just the assassin that many speculate was Joffrey due to some of the things he stated to Tyrion but I can’t remember so we might shelf that and have events go as they did with that.

Let’s assume starting from after the river (or during) is our best course of canon drop-off. I mean Arya still tells her wolf to leave (remember Sansa’s wolf was only killed after the fact that Arya’s wolf disappeared and ‘a wolf had to die’) after it attacks Joffrey, right? Also, where does this leave Arya’s friend who gets executed because he happened to be responsible because of ‘reasons’?

Not sure about Syrio training Joffrey at an earlier or current point in time, but that's a neat idea.

[b]Ned:[/b]

It depends how the conversation goes with Joffrey visiting the dungeons, something he did not do originally. Having a heart-to-heart with Ned despite the Lord Stark pretty much damning them to live through Stannis’ nonsense later on is something that brings an issue.

[b]Sansa:[/b]

I imagine he comes to a decisions after a lot of aggravated quiet contemplation. Also next to her sister, Sansa, must seem pretty unspectacular by comparison as there are few “noblewomen” who have interest in martial pursuits.

[b]Petyr & Cersei:[/b]

Petyr would definitely try to play his game, but I’m sure he would be surprised by Joffrey forgiving/not-executing Lord Stark. As for Cersei I could enjoy how this ends up being written. 

[b]Tyrion & Cat:[/b]

I’d like Tyrion to still become Hand of the King and all of that in Tywin’s absence and inspire Joffrey at the Battle of Blackwater when we reach that point; and since Joffrey might latch onto Tyrion’s wisdom (which would PISS the LIVING SHIT out of Cersei) it turns into a character arc from there.

Also, Robb still marches on the south due to his father being imprisoned right? The whole Clash of Kings plot arc might be something to think about.