I'm only responding here to work through this and see if I understand.
Continuing on the Netflix/Marvel kick:
Daredevil is blind (Situation). The majority of his personal throughline problems come from his inability to stop himself from going out and fighting crime. This causes him huge interpersonal issues, and he wants to stop, but he just can't. So Do-er.
Danny Rand (Iron Fist) is missing and presumed dead, along with this parents (Situation). He returns to New York to find out what happened to them, and repeatedly refuses to take no for an answer when people to tell him to stop looking, even though this causes problems. Do-er.
Jessica Jones has problems from her past as well, but this manifests more in terms of bad memories, impulsive rage, drinking, etc. Overall though, she only starts investigating and digging into her past when those around her push her to do so out of concern for her psychological well being (i.e. you need to deal with your s*&t.) Be-er.
I still haven't watched all of Luke Cage, but my sense is that he is a Be-er -- at the beginning of his series, he just wants to work in the barber shop and keep his head down. He also really tries to avoid violence. But then this could be an Avoid problem or something so I'm not sure.
Does any of this map to things like the "Refusal of the Call" from the Hero's Journey? Or is this just an example of where the Hero's Journey doesn't have the fine-grain resolution of Dramatica?
And none of this responds to your Billy and the Kung Fu School question which I'm not sure about.