I'm very sorry to hear about your situation, best wishes to you....
If you can afford it, I would consult a lawyer. Having said that, here is my take...
If you are current on your loan the mortgage company will not have any options for you, it won't do you much good to talk to them (just talking to them won't hurt though), especially since you don't need any kind of loan modification, you just need out. I would list the property for sale and make a couple more payments. If you have moved already and your finances won't allow paying for it anymore, then stop paying. If you haven't sold it when you get to 60 or 90 days late, the mortgage company will start to listen to you. Try to continue on the short sale route or let the home foreclose. There isn't much benefit to you in either scenario because that kind of mark will keep you from buying another home in the near future, though it seems like you have more pressing matters to worry about. Based on your credit score you are very responsible so it will be really hard on you missing payments, try not to worry about it too much though.
Obviously your score will drop, I can't estimate how much, but if the rest of your credit profile stays healthy I wouldn't be too worried about it.
Bottom line, the world isn't going to end because you get foreclosed on. That is a fixable part of your life down the road. Good luck with your treatment.