I think a project along these lines needs to get done. I am going to repeat ideas others have said that demonstrate that this is a workable idea:
-George Lucas obviously targeted this movie at kids, which is why it didn't appeal to many long-time fans, most of whom were kids when the OT came out (or in my case, an ovum for the first two). While the OT has appeal for both age groups, much of the PT, especially TPM, appeals only to children. I witnessed this firsthand when I took a risk and allowed my children recently to watch the PT, which they in fact enjoy more than the OT :( (my hope is that they'll outgrow it as they mature). But since I enjoy the Ewok films as children's movies, I can see turning this even more child-oriented, and it could be a child's intro to the Star Wars backstory without destroying my love for Star Wars in general.
- Jar Jar is really the best main character. The others rotate and there is never focus, but this can easily be changed with a proper, Jar Jar focused fan edit.
- This is much like the R2/3PO intro to Luke Skywalker of ANH, as Jar Jar could introduce the whole PT to us, and from there we follow the less childish main characters of Anakin and Obi-wan in Episodes II and III (Anakin only being slightly less childish than Mr. Binks).
To accomplish these objectives, I agree with what princethomas has said, with the movie starting with the planet's invasion. I also think a voice intro would be good, though I don't think it means we have to do away with the opening crawl either. I would actually have the intro given by Jar Jar himself rather than the narrator, so if someone is capable of a good impersonation (and I might be that someone, not sure, need an objective listener), then perhaps it could really sell Jar Jar as the main protagonist.
To assist with the opening, the best bet would be to include some shots that were animated, but without any complete rendering available. This would be a compromise, but it would be the ideal way to open with Jar Jar, IMHO.
http://www.youtube.com/watch?v=WfU3T40IVuU&t=25m49s
http://www.youtube.com/watch?v=WfU3T40IVuU&t=24m44s
Interspersed with the complete footage, I know this would look ugly, but it would be a better introduction to our clumsy hero.
Ultimately I would cut scenes that were not so important for character development or story if they did not have Jar Jar, include deleted scenes that served little purpose except for Jar Jar humor (i.e. the waterfall scene), and simply keep him as the focus. As Bingowings said, he could be dubbed to not be so idiotic (since racism is a huge charge against him, though I still believe that is not really true). The tweedy professor sort also sounds interesting, and his voice could be altered completely.
I think there is a lot of potential for an edit like this, and though I lack the talent to do it myself, I think someone should do it.