When the company is not being compensated for transporting passengers or cargo for hire, it's Part 91. In the case of your company wanting you to drop off the Med Crew and ferry the aircraft back to Base, conduct a relief, and then go back and pick up the Meds, neither of the "empty" legs are being charged to anybody, that is, the paying customer...which is the patient, in the case of HAA.
The fact that you are being paid to do this does not make it 135. Neither does the fact that, in the case of a contracted aircraft, the contracting air carrier may be able to charge the contractee a flight hour fee. It's a 91 operation and therefore you can do it legally and the company can ask you to do it legally.
I know you won't understand this, because you don't want to. But that doesn't change the way it is. So if it is an issue with you, please, by all means, the next time you get asked to do this, tell the company you quit. You will be better off, and the rest of the community will be a whole lot better off. Win-win.