I think the primary problem with The Phantom Menace is the tone. The innocent, childlike tone is inconsistent with the rest of the prequel trilogy, which is a dark, tragic tale.

I would tell the tale this way.

Darth Sidious never appears in holographic form. Darth Maul pulls the strings of the Trade Federation.
Battle droids slaughter all who resist occupation. They force the rest to work in labor camps, mining plasma to enrich the Federation.
Fierce racial tension exists between the humans and the Gungans.
C-3PO is Queen Amidala’s protocol droid, not Anakin’s creation.
Obi-Wan, not Qui-Gon, discovers Anakin. Obi-Wan is astonished a little boy is able to instinctively use the Force without any training.
Anakin is a traumatized child slave. He is already able to use the Force but is not able to control his powers. Anakin’s slave master abuses him and his mother.
Obi-Wan orders Anakin to stay on Coruscant, but Anakin disobeys him and stows aboard the ship. Anakin purposefully destroys the droid control ship, saving the day.
Yoda reluctantly permits Anakin to be trained out of a fear that without the influence of the Jedi Order he would become more dangerous.