Landing
Palpatine talking with Amidala
Qui-Gon telling the Council about Darth Maul
Anakin searching for Padme
The Senate scene
Qui-Gon and Obi-Wan talking
Anakin's test
Amidala deciding to go back
The Council deciding not to train Anakin
Leaving
Sidenote: The order of the Coruscant sequence should stay as-is. Having ALL the Senate stuff then ALL the Jedi stuff is too much of the same thing continuously. Let them break each other up.
I agree. The lighting in the various scenes makes it difficult to envision the scenes together. We'd have to go through a full day with Padme, then go back, and watch the same day again from Qui-Gon's point of view (or the other way around). That just doesn't feel right. Plus, cutting straight from Qui-Gon in front of the Council to either Qui-Gon talking with Obi-Wan or Anakin in front of the council seems weird. And, I think by dividing Coruscant into a Padme segment and a Qui-Gon segment actually reduces the emphasis on Qui-Gon. If we follow the order I listed below, I think we keep more focus on Qui-Gon throughout. I think starting with Qui-Gon's story instead of Amidala's makes it feel like the more urgent one.
We're cutting the scene where Anakin looks for Padme, which leaves us with nine scenes. We can't mess with the order to much, because of the light (one of my favorite parts of the movie, actually). But if we can find a shot of the Senate Building during sunset, then we can put them in this order:
Landing (obviously)
Qui-Gon telling the Council about Darth Maul, getting permission to bring Anakin before the Council
Palpatine talking with Amidala
Anakin's test
Qui-Gon and Obi-Wan talking
The Senate scene
The Council deciding not to train Anakin
Amidala deciding to go back
Leaving
ETA: More explaination