Here's my Ep 1+ infinities:
Anakin is already a teenager and the padawan of Kenobi. They are sent to Naboo to settle the Trade Federation conflict. (Note: Palpatine has already had the clone army in development for years, because he plans ahead and such, but nobody knows it.)
Anakin and Padme are love struck from the first time they lay eyes on each other. Because they're both teenagers, duh.
They have some adventures, blah blah blah, they make it to Coruscant. There's a meeting with the Jedi Council. Dooku is a member of the Council. Padme is afraid the Senate won't act on the invasion, and requests that if that is the case, the Jedi respond in force to free her planet.
The Council is divided. We see Dooku arguing that the Senate is corrupt beyond redemption, and the Jedi must take it upon themselves to settle this conflict. But most of the Council disagrees, especially Mace, who says it's not their place to declare war and the Jedi are not soldiers, they can't fight a war by themselves. We see the tension between Mace and Dooku, with Yoda trying to mediate and be the understanding voice of both positions, but ultimately agreeing with Mace.
Faced with the reality that the Council will not help her, Padme has no choice but to call for a vote of no confidence in the hope that Palpatine will be elected Chancellor. This is the last straw for Dooku, confirming his position that democracy is a hopeless mess and the Jedi Council are willfully blind to reality.
Fast forward to Ep 2, just a couple of years later. We now understand why Dooku resigned from the Jedi Order and why he is encouraging planets to secede from the Senate. There's genuine suspense as to whether he's really just a political idealist or has turned darker. It's also revealed that Mace was Dooku's greatest apprentice, and his greatest disappointment. At the end, after Dooku defeats Kenobi and Anakin, it's Mace that shows up and duels him to a draw until Dooku escapes.
Fast forward to Ep 3, when the final showdown between Yoda and Palpatine is the first time we see Yoda bust out his lightsaber and fight. It's one of the climaxes of the whole prequel trilogy.
As an added bonus, we get to spend more time on the romance between Anakin and Padme, which is actually the main plot of the prequels. A major shortcoming of the prequels IMO is that Lucas was so in love with the fact that SFX technology had advanced enough for him to do the world building he always wanted, he forgot that the romance is the main storyline. It's not like the OT where the Han/Leia romance was a subplot. The Anakin/Padme romance is the story of the prequel era, with the other events and world building serving as a backdrop to the tragic love story.