C3PX, I'm not sure if you've read it in this thread, but I've had a similar idea about Episode III and the lava scene. Except I take it one step further, and have Anakin actually die, and Obi Wan sees it happen. Then the Emperor retrieves his body and brings him back to life as Vader (with heavy modification of the construction of Vader scenes so that Anakin's body is motionless). This goes along with my "Power of the Dark Side" idea: it's Vader's loyalty to the Dark Side that keeps him alive. If he betrays his master, he ceases to live. If you think about how Obi Wan talks about Anakin in the OT, and how Vader says he must obey his master, this starts to make a lot of sense.
About the birth scenes in Episode III, I think the entire scene should stand as it is, with the exception of Padme naming both the twins. It makes no sense to have her name Luke but not Leia. The scene aboard Tantive IV is weak anyway ("Yeah, let's hide him with his family and let him keep his last name. Great plan!), so the entire discussion of the twins' fate should go, including "My wife and I have always wanted a daughter." (Maybe the tail end of this scene can be saved, where Yoda tells Obi Wan about his training on Tatooine.) Luke can be dropped off (it is a beautiful scene, and a good one to close on), but not Leia.
Musicman, I'm not positive, but I don't think Leia is referred to as Organa in ANH.
I would love it if Leia could not be Luke's sister (sorry to step on your EU, people). But I think it will be very hard to pull off. I don't see how Leia and Han can have any kind of reolution without it. Han should have died, but he didn't. We have to deal with that and work with what we have. So Han needs some kind of resolution.