Although he was only introduced and killed off in TPM, I think there is an interesting conceptual direction that a writer can take the character of Qui-Gon Jinn. Normally I don't like using elements of the Lucas PT in my brainstormings, but he comes the closest to being interesting out of all the Lucas PT's characters. My idea for an alternative Qui-Gon is called "Templar Jinn".

He's an elder Jedi who becomes obsessed with rooting out and exterminating the Dark Side of the Force. He accuses the rest of the Jedi Knights of being complacent in their quest to bring peace to the galaxy, primarily because he sensed the hand of the Dark Side in the events of the Clone Wars (which would be a completely separate event from the rise of the Empire in my timeline). He goes rogue, a light side fundamentalist, basically.

Anakin Skywalker goes on a quest to find and capture Templar Jinn before he can further tarnish the name of the Jedi Order. But when Anakin gets there Templar Jinn refuses to be taken in again and they have a lightsaber duel. It is this lightsaber duel which irrevocably starts Anakin down the path to becoming Vader. After a lengthy fight, Anakin cuts off Jinn's arm.

The mortally wounded Jinn lays upon Anakin a revelation which is just as mindblowing as the I-am-your-father thing that Vader said to Luke in ESB. I'm still trying to figure out just what this revelation might be, but it has to be something that completely sours Anakin's opinion of the Jedi. Then Anakin executes the maimed Templar Jinn. I envision this fight being the climax of Episode II.