ojay,
To watch the automation like a hawk you have to know what you are watching. Your scenario obviously precludes all non precision approaches. But then, an ILS that is not certified for Cat II/III operation is possibly either higher, lower, curved or a comination of these. As long as you are on this high, low or cuved ILS your ILS indications on your flightdeck will be centered. The A/P is just doing its job: It is following the same radio signals you see on your instruments. The only clues you may have are DME distances/Altitudes, powersettings and vertical speeds. To monitor all this may just be a little too much if you are in a hurry to get a patient down and at the same time flying a bumpy or curved ILS in lousy weather. So I have to agree with JJM; for me a return is out of the question for this scenario.
I can however imagine a scenario where I would bust minima. A thing I learned from an old instructor long ago is that if you must crash, the best place to do that is on an airfield. That's where the fire engines are closest.
Capt PPRuNe, my chief prescribes 1hr flying to T/O alternate for a twin.
So 777 I think my patient would have to hold on for another 40 minutes at least.