Let me give you an example within the natural sciences... according to the literature, acupuncture works really well in China but very poorly elsewhere. This seems unlikely to represent an underlying reality based on analysis and review of a wider body of literature and our knowledge of how political power and personal expecatations distort content. So the best explanation is that it's an artefact of the culture that produced the publications.
(...)
The progress has been gradual, though: Drs. Novella and Hall are certainly model skeptics, and this higher-level analysis is the underlying motive for pushing "science based medicine" as an augmentation of "evidence based medicine" - it's an acknowledgement that the scientific literature can't be taken at face value, but has to be analyzed in social context.
I think this is a profound misunderstanding of science and scientific literature. There is no "social context" that needs to be considered. All that matters is scientific rigor, something Postmodernism falls far short of.
Your example of acupuncture in China is also fails. The best explanation is not that it's an artifact of culture. The best explanation is that it's most prevalent in China due to an accident of history making China the origin of the practice, and the lack of scientific rigor in the studies that supposedly show its efficacy. It's only cultural in that China does not have the tradition of objective observation and experimentation that has formed the foundation for Western scientific exploration since the Enlightenment. However, many of the studies which found greater efficacy were not necessarily Chinese in origin; but were conducted by westerners who also lacked the necessary scientific rigor; and their findings fit well within a Postmodernist framework.
Postmodernism is, at it's core, a rejection of pure objectivity, or at least a de-emphasis on the possibility of objectivity and focus on subjective experience. The problem with trying to define Postmodernism beyond that is there is no coherent philosophy or methodology to rely on. No set of core philosophies or methodologies that one can point to to differentiate "real" Postmodernists from outliers. In fact, the very foundation of Postmodernism denies such a foundation is even possible; and "outliers" are simply taking principles to their logical conclusion.
The skepticism you've claimed as the purview of Postmodernists did not originate with the movement, but in fact originated with the Enlightenment and came into prominence with 17th century Rationalism. Postmodernism did not contribute the concept of skepticism, that originated in Enlightenment thought. What Postmodernists did was misappropriate the concept, and re-defined it to mean a rejection of the possibility of objective observation and evaluation of claims and assertions, in favour of a subjective focus on the claimant entity itself. Postmodernist "skepticism" is the opposite of scientific skepticism, the entire purpose of which is to minimize, if not fully eliminate, the effect of observer bias and subjectivity, and arrive as close to objective truth as is humanly possible; re-evaluating conclusions only as measurements become more accurate, and observations more objectively demonstrable.
That is why Postmodernist thought has grown up primarily in the Humanities, where subjectivity has free reign. It has managed to infiltrate the "soft" sciences, where objective observation and metrics are more difficult to obtain; but has been soundly rejected by the "hard" sciences.