^That's an interesting idea. Instead of a split personality, though, it seems it would be better to somehow label Anakin as Palpatine's secret assassin, going on missions that the Jedi aren't even aware of, and that he uses a code name of Vader, or something like that. He's already engaging in questionable actions, but the Jedi are unaware, and he still sees himself as a good guy.
Now that I said this, I guess this does nothing to preserve the "I am yo' daddy" surprise, but it perhaps makes his fall more believable and gradual instead of so sudden....
....Perhaps the opening crawl could indicate that Palpatine has begun to unleash several clandestine assassins throughout the galaxy to eliminate dissidents, that there is a rumor of a man named Vader wiping out political opponents, and also mention that Anakin has joined the ranks of his assassins, though the wording implies that the two are different. Somehow throughout Ep III itself, an editor would have to make some minor allusions to Anakin's secret activities, but it seems a little dubbing might suffice. Anakin would think he's enforcing order in a galaxy gone mad, then realizes the Emperor is a Sith. He goes to face him and gets zapped.
But jonathan7, even if we managed to get this far, what would we do to show Palpatine unleashing lightning upon him, explain Palpatine's facial deformity (I wish they never included that in the first place), and explain why Mace never shows up again? As you mentioned in the other thread, it would be necessary to insert an armored Vader into the fight with Obi-Wan and explain that too.
It's an interesting idea, but I'm still wondering about other parts of it. I'd hate to lost the Obi-Wan/Anakin fight and the damage he receives because of that fight. I was thinking maybe some parts of Mustafar could be moved to earlier in the film, maybe even showing Anakin taking out the Separatist leadership as part of his assassin duties before his actual true fall to the dark side, but how would he get back there? I dunno, maybe I just can't have my cake and eat it too. But I feel there's a lot of potential to your idea and would hate to give up on it. Keep brainstorming!