I've done air ambulance work in Senecas, King Air's, and in Learjets. Some domestic, some international. Most of my flying involved airplanes that were very well equipped with everything that one would have available in a hospital emergency room...including experienced and trained personnel.
I have been out of my seat on the ground, covered in vomit and blood in the ambulance while we tried to get a patient on board, because we ran out of hands in the ambulance. One one occasion when it was bad enough the ambulance driver, one of the emergency technicians assigned, got scared and ran away. I've flown terminally ill children, cancer patients, women in labor, auto wreck trauma victims, gunshot cases, infectious patients, and even a chainsaw to the face.
I once had an individual in the right seat of a Seneca II, who was being taken home from a hospital to a remote location. As this was ad administrative transport, the nurse was not aboard; just me, the patient/passenger, and his wife or girlfriend, in back. Night time, with convective weather around, he had a heart attack. I'm an emergency medical technician (or was; I'm lapsed now), but there's precious little one can do while flying. The patient was a largish gentleman who collapsed forward, unresponsive. I later learned he was a cardiac patient coming home from some tests, not simply someone being transported from A to B. What was a simple flight became complicated in short order.
In the US, an organization called "Angel Flight" has been operating for many years. It consisted of a number of volunteer pilots who would move patients from A to B at little or no expense, using light airplanes. The idea was that many people couldn't afford the costs of the transport, and thus this was a real blessing for them. It's been done successfully for some time. You may be able to contact someone associated with that for direct counsel on what they do.
For my end, a simple transport of an medical patient can become dire and complex, very quickly. You're not close to immediate help. You're taking a patient that is impaired, ill, or broken in some way to higher altitude with lower pressure and oxygen, and placing them in a remote environment under some degree of stress. In a light airplane that can be for some time.
When people say they won't sue you legally, that's fine, but remember that it's the deceased's estate that sues...and that doesn't begin to exist until they're dead. Even the deceased can sign a waiver saying he won't sue...but that's no longer valid after he's gone, and he can't sign away the rights of the estate because it doesn't exist yet...so the signature does very little good if he dies or becomes incapacitated or injured as a result of the trip.
Personally, when doing ambulance or medical transport flights, I've always felt much better knowing that there are people in back to whom I'd trust my life, who are trained, experienced, and equipped to care for the patient...because no matter how qualified one may be, you cease to be of much help to the patient when you're the pilot. Your job at that point is to get the patient/passenger safely to the destination, not to work on the patient. Far, far better to carry others on board who can do that.