Postmodernism and Biblical Hermeneutics is an interesting issue.
I think we have to be careful about drawing conclusions about the sources for stories based on the content of those stories. For example, consider the Temple Cleansing story and the plethora of possible source-explanations for it. The historical verisimilitude of the story is in question because there would have been guards at the temple specifically to prevent such a disturbance as Jesus is depicted as starting. So:
(1) Maybe the story is accurate and Jesus caused a small disturbance at the temple that didn't alert the guards..
(2) On the other hand, maybe the episode never happened, because there would have been guards there to prevent such a disturbance. Maybe Mark was part of an anti-temple sect like the Qumran sect and so was presenting in the story the idea that just as it was no longer the season for figs (the withering of the fig tree story), so too was it no longer season for the temple (the temple tantrum being sandwiched between the fig story).
(3) Maybe the story started out as a sermon Jesus liked to give about the corruption of the temple, and that sermon simply morphed over time into the temple cleansing episode that Mark inherited.
(4) Maybe the temple cleansing episode started out as a dream someone had about Jesus, which morphed, over time, into the temple tantrum story that was passed down to Mark.
(5) Maybe Mark was apologetically justifying after the fact that the Jews really didn't need the temple, in the wake of its destruction by the Romans
(6) And this could go on indefinitely ...
Anyway, postmodernism's point is that when we draw conclusions about sources that lie behind narratives we need to be very careful, because often times our choices can just be wishful, lazy thinking.
There's nothing new in the postmodern approach of those like Derrida (deconstruction) and Heidegger (destruktion). For instance, Kant is going to find something in Hume's philosophy that is going to threaten to overthrow Hume's position. Deconstruction comes about when something a System is trying to appropriate resists, and threatens to overthrow the system. For instance, there is going to be something about LGBTQ rights/love that is going to threaten to overthrow the traditional definition of marriage, and cause that definition to be "de-constructed," and then provisionally "re-constructed" in a more inclusive way. As Derrida says, Deconstruction is Justice. The methodology is very old. It's what Socrates did going around Athens and testing/questioning people's definitions.
Sometimes when we are in the Meaning Making Process (in hermeneutics generally, not just biblical hermeneutics), there is polysemia, especially when the evidence is scant and ambiguous. My favorite example is by American Philosopher John Searle. Searle offered the following thought experiment:
"I was walking by the beautiful, bright window with an adorable dog peeking through. I wanted it." - Searle asks: Does the person want the dog or the window?
People sometimes confuse the idea that there is an objectively right answer (the person EITHER wants the dog OR the window), with the problem of whether we can epistemologically be confident in the scenario we choose as correct.
Hermenteutics involves humbly proposing a model that explains the evidence, and deals with any apparent recalcitrant evidence. But we must always accept that some of the evidence may be ambiguous and thus open to multiple interpretations.
Of course, this isn't the same as saying anything goes (e.g., claiming a reasonable explanation of the evidence is that the tomb was empty because Jesus was beamed up into space by aliens and the disciples were then regaled by the aliens with holographic images of Jesus, lol).
And I think we should acknowledge the issue that multiple attestation doesn't necessarily mean independent attestation. For instance, the "Love Commandment" is present in all four Gospels, and Paul. Maybe this is because the Historical Jesus taught Love over purity. On the other hand, an emphasis on love in Matthew doesn't mean an independent source, since Matthew read Mark. And, an emphasis on Love in John may simply mean John read one or some of the synoptics, or that some of the ideas from the synoptics were floating around John's community when John wrote. As for the presence of the Love Commandment in Paul, maybe this goes back to the historical Jesus, or maybe it was Paul's invention and Mark (having read Paul, or Paul's ideas just floating around when Mark wrote) put Paul's love commandment on Jesus' lips. Or, maybe Cephas and the gang came up with the love commandment after Jesus died, and this is how Paul was exposed to the Love Commandment. And these plausible scenarios could go on indefinitely - as Postmodernism points out.
Postmodernism rallies against the conception of Truth as certainty, freedom from doubt (birthed from Thomas to Luther, and canonized in Descartes), and operates by not being satisfied with what seems "obvious," and trying to restore weight to ignored, marginalized, alternative paths. Didier Franck provides a useful summary of the genesis of modernism (the transition of verum into certum): “No doubt, Descartes transferred to the cogito what Saint Thomas, who placed certainty of faith above that of knowledge, attributed to divine science alone.” Further, Descartes took as his model Luther’s characterization of what had to be certain: certainty as freedom from doubt regarding the salvation of the soul, which left Descartes with the cogito as certain, that is, free from doubt. From there modernism blossomed beyond the antinomies of Kant (EITHER/OR), the dialectic of Hegel (BOTH/AND), and finally into postmodernism with destruktion/deconstruction of Heidegger and Derrida (NEITHER/NOR)
I think the goal of Postmodernism is fundamentally ethical. As we begin to deconstruct the "obviousness/certainty" of our beliefs, ignored, marginalized voices are given space to emerge, grow and flourish.
Postmodernism is basically about testing our assumptions to see if there are perspectives which are unfairly marginalized. For instance,in the past, and to somewhat of a degree today, it was "obvious" that that marriage was between one man and one woman. Over time, voices called out for the traditional understanding of marriage to be deconstructed because it was marginalizing LGBTQ individuals, and so marriage is beginning to be deconstructed/reconstructed in a more inclusive manner. Still, even this new definition may need to be retooled to include Poly-relationships (e.g., polyamory, polygamy, etc.).
Derrida says that when we choose (an action, an interpretation, etc.), it is a Kierkegaardian leap of faith, because in deciding to choose there is never enough time, precedence, information, because we can always be wrong, and there is the possibility of unintended violence. The point is to make our choices in humility, and always be ready to revise and refine our positions if new information comes to light. I don't mean that any interpretation goes - like, as I said, the tomb was empty because aliens beamed up Jesus' body and then the aliens regaled the disciples with holograms of Jesus, lol. My point was just one about humility and responsibility in our choices. And sometimes the evidence is more scant and ambiguous than we realize, and so polysemia can be a real possibility in certain cases.
Of course, a further problem is that Jesus never wrote anything, so the issue arises, for example, how do we tell when Mark's Jesus represents the historical Jesus, and when Mark simply hijacks Jesus and uses Jesus as a mouthpiece for Mark's theology/purposes. Philosophers encounter a similar problem when they try to entangle the historical Socrates from Early Plato.
So too do we need to be careful when we, as Ehrman does, infer that a writer has new sources because there is material unique to his gospel. For instance, as Carrier points out, there is new information communicated about Moses from later writers outside canonical sources, but we would not infer these later writers had new sources that went back to Moses. Similarly, it would be a paralogism to conclude that just because Luke has material unique to his Gospel, that this material reflects a unique source - let alone one that goes back to the historical Jesus (especially given the way we know Luke invents material for Acts, given that we can fact-check Acts against Paul's letters - much is assumed, for instance in Mark, because we have no documents to fact-check Mark against).