I refuse to give up on the idea, and I know that the window of opportunity is only a few months.
  I am considering outsourcing the development to India, so I can get it to a releasable state.

Since the window of opportunity is only a few months, i would strongly suggest not to look at the outsourcing option to India (or anywhere else). One, you would have a difficult time in finding out the right set of people (skill wise). Two, establishing a good working relationship takes a bit of time, especially working across geographies. A small startup pushing towards it's first beta is probably not the right time to start using the outsourcing model. (Side-note: I am a developer based out of India)

You have got a lot of good suggestions on the way forward from here. I would also endorse you seeking out the Django experts on this forum who have offered help. At the bare minimum, they can review the code and tell you where exactly you are and how much more effort it would take to make a beta release.

Alongside, you can get some legal advice on getting out of this partnership with the least possible damage to you and your ethics.

Learning to code obviously would be helpful, and it really ain't that difficult.

Don't worry about this temporary setback, just get back up and give it a shot again. Being in the medical field, am sure you would have seen people fighting and coming out strong from far more difficult situations.

Good Luck.