Well, Joffrey was still an insufferable classic chaotic evil when he saw Arya practicing her swordplay with the Butcher’s kid. Now while even if I made him more competent “suddenly direwolf” still gives him a big disadvantage. But instead of being a whiney little twit I decided he’d have this strong sense of pride that he’d not tell anyone he was bested by someone like Arya. I also spun an idea that this is where he initially got a little intrigued by the younger Stark daughter. So, that would obviously change events though I’m certain him peckishly hiding a wolf bite due to his sense of honor would make Cersei livid when she found out. 

1 > 3 > 2 would be my preference of your ideas.

Definitely willing to write this. Though I ponder how we'd keep it interesting.