I just registered because I had some thoughts on reworking TPM. Some (if not all) are probably repeats, but I thought I might share anyway. I am very tempted to get into the game and try and make an edit myself.
First of all, I would rework the whole narrative to have the Tatooine sequence first. The scroll would establish that the Queen is on the run from the Trade Federation, with two Jedi protectors. Padme wouldn't be a handmaiden or even the Queen, but would just be someone in the Queen's party. She accompanies Qui-Gon to Mos Espa with no argument about it. Jar Jar is established beforehand in a reworked scene with Padme cleaning Artoo (implying Artoo is her personal droid, thus why he accompanies them to Mos Epsa). The Gungan/Nubian dynamic is established then.
During this sequence, we would be introduced to the Trade Federation through watching them initiate the invasion of Naboo. Sio Bibble would be portrayed as the main Naboo character on the ground. Sidious would appear somewhere in here, not sure where, but done after Maul's first appearance on Tatooine.
Anakin won't really be the hero (or even much of a main character) in my edit, much to chagrin of some people around here I think. Most of his Tatooine exploits will remain the same, with the addition of the Greedo scene before they leave. Maul's first appearance, and the first appearance of the Sith, would be his arrival on Tatooine.
Once they leave Tatooine, they'll head to Coruscant, where Anakin is given to the Council for testing. Anakin will only show up in the testing scene later on, which would be intercut somewhere in the later Naboo sequences before the battle is underway, the funeral of Qui-Gon, and the final scene with Obi-Wan. Palpatine would already be played as being the Chancellor, since the Senate sequence would be cut due to Padme not being the Queen. His inability to get things done would lead Padme and the Queen to go back to Naboo to fight. The Nubian senator would not be relevant in this edit, although it could be assumed it is Valorum since he appears in the first Coruscant sequence.
Instead of the Nubian's asking the Gungan's to help them, when Jar Jar speaks about them not giving up without a fight and being warriors, it'd cut to the Gungan's marching to war. Jar Jar would obviously be cut out of this conflict as he wouldn't be there (nor would he show up until the ending sequences either). Padme and the Queen's struggle now comes to get to the throne room and force the Viceroy to surrender and stop the droid army. The space battle would be cut entirely.
Since the Control ship isn't being destroyed, the Jedi slip into the control ship, with the idea of getting to the bridge, using the first sequences of the film. However, they encounter Maul, and their duel takes place on the control ship.
Once Padme forces the Viceroy to surrender, the droids are shut off, the Gungan's celebrate, while the Maul/Kenobi duel finishes up. Yoda informs Obi-Wan that Anakin will be trained (he will not be rejected in this edit), but informs of his misgivings.
The idea for this came from my thought that Naboo should not be visited twice in this movie by the Heroes. Once they leave a location, they shouldn't return in that movie. Everything else flowed from there. Just thought I would throw the idea out there and see what others thought. Feel free to co-opt anything you find good.