Aalenfae, you mentioned getting Padme to Alderaan: what about Padme delivering the twins on Alderaan in the first place? (haven't figured out all the details of why is she dying, and could this work with Anakin Jedi hunting before Mustafar, etc - but who better to figure those details out than this group...)
I actually don't think a reason needs to be given for how and why Padme dies. She goes to Alderaan in hiding with Bail, and we can assume from Leia's words in ROTJ that she dies young from grief. This happens in "real life" as emotional and mental stresses can cause people to just let go... Sometimes everything doesn't have to be explained to still be a good story :) That way you can also do away with Medical Droid lines completely if you wanted to.
Side note: Anakin's dreams of Padme dying in childbirth don't have to become a reality to still have an impact emotionally; enhanced by the fact that she lived (if on Alderaan) while he thinks she died. Also thinking logically, Anakin's dreams, from his point of view, never became a reality since he killed her before she gave birth.
Regarding that vision: a view that came up with discussions amongst my friends was that those dreams were planted there by the Emperor to encourage Anakin to seek the power needed to save her. They weren't necessarily completely true or only his to begin with - perhaps the Emperor just expounded Anakin's own fears of loss? Again, in my opinion, it doesn't need to be explained to be good.
Keep up the great work Aalenfae! I know we're all looking forward to seeing your progress as things develop!