Another thing to consider is Anakin's dream. He says she would die in childbirth. Granted, his dream doesn't need to be literal. As Yoda says, "Always in motion is the future." But I like the idea of the self-fulfilling prophecy. Maybe the dream could be altered to show a death somehow due to illness. Maybe this could set up the idea of Padme falling ill without coming out of nowhere at the end of the film. This could possibly involve changing Anakin's dialog when he informs Padme of the dream.

3. Perhaps her injuries at the hands of Anakin could have something to do with it. Might explain things a little.

Yes, that would be most desirable. Serious brain injury can result from a choking, as happened to this reporter who was strangled by a vet suffering PTSD. However, this wasn't a terminal illness. Perhaps the medical droid could say something along these lines:

Medical Droid: The strangulation appears to have cut off blood flow to the brain, damaging it permanently, and destroying the ability of the body to repair itself. Unfortunately, it is too risky to perform surgery. We estimate the odds of survival beyond one year to be 1:10. Given the odds, we recommend delivering the babies as soon as possible.

edit: Another idea is to have the brain injury destroy the regulation of the heart, weakening it day by day. This plays into the metaphorical "death of a broken heart" Lucas went after.