I don't think you've done enough work to defend the introduction of the concept of post-modernism, here. I suppose postmodernism does include the proposition that one cannot be certain of anything but there is no particular reason to adopt the addition baggage that comes with the concept. The proto-typical enlightenment philosopher, Hume was already there. So what does postmodernism add? The term, without any further explication makes this post very difficult to follow as I have no idea what exactly you mean.

Moreover, it seems to me there is a rather straightforward point of tension between postmodernism and Bayesianism, namely that Bayesian prescribes a uniquely rational way of structuring belief networks, which certainly looks like the kind of self-assured epistemological approach that prototypical postmodernists would resist.

I think what you're actually seeing is the complementarity of Bayesianism and Quinean coherantism/pragmatism. The latter, I suppose is closer to the postmodern tradition than, say, logical positivism. But it is a far, far, cry from the Rortian position that the only constraints on knowledge are conversational and socially constructed. Is your position that the restrictions Bayesianism places on the beliefs we hold are merely socially constructed?

Which is to say, if you want to examine the relationship between Bayesianism and other philosophies it really helps to actually identify the other philosophy instead of just talking about the vague and routinely contradictory clusterfuck that is postmodernism.

And in the right light Derrida can look like anything.