It might be fun to see someone try this in an edit of all three films: https://www.reddit.com/comments/3qvj6w
It would mean taking all the Jar-Jar footage and spreading it over 3 films or making new Jar-Jar footage. But it would be cool to actually do the character well rather than just cutting him out.
Frink actually does a good job at giving him some kind of wacky dignity but this would be an interesting alternative. He could replace Maul and Sidious as the power behind the events in the first two movies at least.
Heck it might even be possible to have him replace Grievous 😄