Well, one thing does come to mind and surprisingly, no one seems to bring this up: the opening of Episode III (aka the battle over Coruscant).

Think about it. This gives the perfect set up for the fall of the Jedi and the rise of the Empire: The chancellor was captured, the Separatists invaded the the capital of the Galactic Republic and the Republic's fleet was probably put into disarray after that battle. Instead of looking at any repercussions of this, what we got was the rest of Episode III.

What I would do is keep the opening (barring some small exceptions like Dooku's death), but show the aftermath. Here, the public is paranoid about another attack and distrusts the Jedi for not foreseeing the invasion in the first place. The Republic wants to bring the full fury of the Republic's military on the Separatists, but the Jedi advise caution, creating a barrier of mistrust between the two. Anakin is caught in the middle as he sympathizes with the Republic and wants to end the war.

Palpatine would use the situation to strengthen his grip on the galaxy and have Anakin slowly turn to the Dark Side. The Jedi, seeing past Palpatine's plans, would try to stop him. They fail, of course, and the Jedi are hunted down. The movie would end with the duel between Obi-Wan and Anakin, now christened Darth Vader (not as fancy as the one we got, but still epic).