One point I mentioned in my last post on the prequels deserves a little expansion. I argued that it's implausible for Anakin to have built Threepio as "a protocol droid to help Mom." Unless Mom is working with binary load lifters or doing serious intergalactic training, this doesn't make much sense. Threepio is, as he says himself in Ep. IV, singularly unsuited (materially, temperamentally, operationally) for a desert climate. And we see lots of droids in the original Trilogy who look basically identical to Threepio. Anakin building a standard protocol droid from a kit just doesn't seem very impressive.
Anakin building R2-D2 makes a lot more sense. For one thing, R2 knows his way around Tatooine. It seems even in Ep. IV that he's been there before. For another, Anakin is a slave, mechanic, and pilot. He needs a versatile Astro droid a lot more than he needs a protocol droid. It would be a great nod back to Jedi if at some point in the first prequel, R2 were carrying a tray of drinks.
So where does Threepio come from? Well, if you take my general treatment of Prequel #1, where Padme discovers the clone army and is met by Obi-Wan, Qui-Gonn, and a young Anakin, we still have to account for how Padme is able to contact Yoda and the Jedi Council to send for help. So, it's obvious -- she sends the message by way of her protocol droid, C-Threepio, who then (much to his chagrin) has to guide the two Jedi, the pilot Anakin, and his sarcastic droid R2 back to her location, where they face off against Darth Maul, etc.
This, I think, would definitively solve the Jar-Jar problem. Jar-Jar Binks's function, particularly in the first of the prequels is essentially identical to Threepio's in Ep. IV (and if he'd been well received, probably would have continued to be basically identical throughout). He's a sometimes obnoxious coward who becomes a kind of reluctant hero, and serves as comic relief. The only problem is that he's unsympathetic, poorly animated, unfunny, and more than a little racist. So why not go with the tried and true? Threepio, especially in his back-and-forth with R2, can be both the comic relief and the familiar still points around which you re-construct this world.
This also, I think, restores R2 and Threepio to the central role they play in the original trilogy, and explains their bond to each other and to Luke and Leia. R2 is their father's droid; Threepio is their mother's. In their own way, the two droids are both siblings, children, and parents to the family Skywalker.
P.S.: You might note that I slid Qui-Gonn back into the story, after I'd basically cut him out in my first treatment. Well, I had a chance to watch The Phantom Menace again a couple of days ago, and Qui-Gonn is the best thing in the movie. He's the only person in the entire trilogy who actually seems like a Jedi: an intelligent, humane warrior with a warm sense of humor, in the best tradition of Obi-Wan in Ep. IV. And Liam Neeson can act. I would still cast Qui-Gonn as the partner, not the teacher of Obi-Wan -- Obi-Wan always says that Yoda is his teacher, and Ben has got to get old as hell somehow -- who discovers and begins to train Anakin, who is killed by Darth Maul and bequeaths his training to Obi-Wan, who Yoda doesn't think is ready. (Not because he's young, but because he's reckless -- "So was I, if you remember.") You can also, assuming that Padme is somewhere between Obi-Wan and Anakin in age, but if they're all adults, set up the jealousy that helps Anakin foster his resentment. The second movie would then show how Obi-Wan fails in his mentoring of Anakin, Anakin slips to the dark side, they duel, and... you know the rest.