As I did my research, I reasoned that a Dragon Dictation-esque solution may be best. However, such a solution already exists. And built by Dragon Dictation too, coincidentally.
It's a very efficient solution for doctors in case #2. They can just dictate their patient notes to an audio recorder, and the software is intelligent enough to sort it out appropriately, with perhaps 80-90% accuracy. However, for patient records, you need to have it at 100% accuracy, otherwise you could face medical malpractice. So the current products require doctors to review their notes on a confirmation screen on their handheld tablet devices (yup, it's on a tablet device much like an iPad). The result? Most busy doctors just hit SUBMIT without reviewing their notes, and their 80-90% accurate patient notes get recorded. Medical groups saw this behavior and have been moving away from these types of products.
I'm gleaming over a lot of details, but this is the gist of what I found. This is definitely a problem begging for a solution, so I wish DrChrono a ton of luck in solving it.