What if Qui-Gon hires Jar-Jar as a guide when they reach Tattooine? Jar-Jar leads them to Watto's shop. Later, Jar-Jar sells them out to Sidious, and stays on Tattooine, never to be seen in the story again.

It gives him a story purpose for existing, and gives Sidious a reason to send Maul there. I don't know how I can make it work, as I'll need to create a scene where Jar-Jar sells them out. Hmmmm...

There's only two ways I can see Jar-Jar functioning in this film:

1. The idea described above, where I try to manipulate it so that Jar-Jar sells the Jedi out to Sidious.

2. Somebody helps me rotoscope him out of the shots I can't crop and he just gets cut altogether.

I don't know how realistic either idea is, but that's all I've got right now. I know that I don't want what I have right now, which is a random character walking around with the main characters not saying or doing anything.