Look, I know it's radical, and if implemented it would turn the entire structure on it's ear (and this project is an opportunity to do that), but...
Let me ask you this, have you ever considered starting the movie with Anakin and Padme already having been seeing each other in secret for some time? The assumption would be they somehow kept in contact over the years and had been having sort of secret love affair here and there when Anakin can get away, and then Palpatine knowingly and conveniently "suggests" that he and Obi-Wan go on this mission to protect her. This would eliminate SO much crappy, doting exposition. Most of the exposition would now rely on subtext, knowing glances. It would shut them both up without shutting the audience out of their character.
The fact is, Han and Leia never talked that much. They didn't need to. It was all in the subtext. "I love you." "I know." And so did we without a bunch of needless dialogue.
It would also change the central question of the film from "will he GET the girl?" (because it's inevitable he will), to "if he LOSES the girl, how will he get her back so they can get married and the twins can be born?"
This would make their emotional connection to each other much stronger. It's an opportunity to make Anakin more of an adult who's in an adult relationship instead of a whiney stalker-boy. It would also make Padme a little more willing to accept things like "If it works..." or "I killed them all" because now she's known this kid for ten years and she has much more emotionally invested in him. You don't have to lose the romantic scenes because it can be the first time they're together without having to sneak around. The scenes are essentially the same, but now they're in a completely new context.
The threat of their separation throughout the film becomes the silent villian and the moment when they do get separated at the end would be much more dramatic. In the hangar, Anakin rushes in to make quick work of Dooku because what he really wants to do is to go back and save Padme, and in a way, to show Obi-Wan he could've handled it himself. Remember, at this point he doesn't know if Padme's hurt or dead, and he won't let happen to her what happned to his mother. Unfortunately, since Dooku is a Sith Lord, it won't be quite that easy.
By the end of the duel, and I can't stress this enough, it is absolutely essential to the arc of the story that Anakin does something that changes the way Obi-Wan looks at him, and allows Obi-Wan to begin to treat him as an equal, paving the way for the growth of their relationship to what it becomes in ROTS. We never got that in AOTC. We got all this build-up, but ultimately no payoff for that story thread, which in my opinion amounts to nothing more than contempt for the audience.
Anyway, I know it's a whole new way of looking at things, and I don't know if it's even possible, but it's just another suggestion to consider and an opportunity to restructure the entire narrative.