1) No part 91 reposition legs per the FAA legal interpretations. That’s black and white. Starts 135, ends 135. With medical crewmembers on board!
2) No one way flights. If you cannot plan to complete the flight with a return to base (hub rule similar to 121 operators) you can not legally except the flight. With medical crewmembers on board!
3) if you accept a legal flight under part 135, then you can complete the flight with an RTB (hub rule) even if it exceeds 14 hours after you initiated the flight. Again, no need to drop off crew because you can legally RTB under part 135. Also, no need for RON. A legal flight could end at an away location, with medical crewmembers on board!
4) All part 135 duty assignments will be used to calculate duty period compliance. That means ALL duties. Post flight, etc. you are on and within your duty period whether part 91 or part 135 until you are relieved if ALL directives by the Certificate holder For the assignment you reported for. A 12-14 hour shift, that can be extended. With medical crewmembers on board.
5) rest period starts when relieved of duty, not at the end of the part 135 patient drop off leg. Always been the case, even for the Part 91 leg back to base afterwards without medical crewmembers on board!
Your 'story' is not the whole story