Thank you so much, this is really helpful.
I do agree that "necessary" is kind of a binary term -- a thing is necessary, or it isn't. I guess that's why my attempts in #0 sounded rather "off." I was also trying to capture whatever German meaning made the word "zwingend" (ahem) necessary to the text, but I think it's one of those cases where the commonly used German phrase has more than the English version requires.
#10: I did a search and got lots of hits for "zwingend medizinisch notwendig" and several for the entire sentence, so I suppose it comes from some official guidelines from the social code or the health insurance industry -- possibly written "by committee" (ie, too many people involved), which would explain the quality of the writing!
PS: I got curious about that last bit and looked up "Krankenfahrten" (the topic of my text) in the Sozialgesetztbuch (SGB), and found:
"...wenn sie [...] aus zwingenden medizinischen Gründen notwendig sind."
Would "aus medizinisch zwingenden Gründen" be better? (I would think so, but I'm no expert.)