If an edit of this kind were to be attempted there would be a lot of Qui-Gon dialogue removed which might be remixable to create the necessary (and only the necessary) exposition.
Oh to have a portable Liam Neeson at hand.
Lines like "I have encountered a vergence in the Force" could be (though I'm not underplaying how difficult the process might be or how awful the final results might sound) altered to say something like "There is something else behind all this, I sense a vergence in the Force" when Qui-Gon and Obi-Wan receive their assignment to protect the Queen.
That way they would be preemptively expecting to encounter this Chosen One on their mission before we find out that he is just a slave boy on a planet they didn't expect to be marooned on. It would actually make something of the somewhat bolted on Chosen One story thread.
A bit like in ESB where the great Jedi Master turns out to be a strange little green guy with big ears.
The discussion about Sith Lords (if it is necessary at all) could be moved to when they have the ship up and running and take place via holograph (like Obi-wan's warning about Geonosis in AOTC).
George created this universe with holographic telephony and precognition but in TPM he felt the need to shift characters across the galaxy to deliver plot points to each other in person. Even in Shakespeare some messages are delivered via messengers rather than having all the characters on stage at once. In most tellings of King Arthur and as far as I know every telling of story of Jesus Christ we know about the Chosen One before we meet him in the story but in TPM we have to find out about all this after we meet Anakin which is one of the reasons it just feels shoved in.
It would need someone or some people to go through the script and see what lines need to be shifted and if they can be re-mixed in a credible way.
The real drawback being that, despite bold claims there is, as yet no scoreless sound mix so John Williams lovely music (not to mention all the various sound effects) may be a real bugger to filter out (if it is indeed possible at all).
Even then joining one piece of dialogue to another and finding a way around lip-sync miss matches is another real task but if it was easy I have no doubt someone would have done this sort of thing already.
As always all suggestions along these lines are welcome.