It seems like you agree with the Illuminists, at least about the potential for conspiracies in science. What you call the "reductionism" of math I call the evocative, game-like nature of math, following Smolin.
We've talked about the Big Bang Theory before. I'm not qualified to assess the details of the theory, nor am I particularly interested in doing so. I'm more interested in the big picture, the philosophical level. The bigger question, then, is the extent to which scientific methods of investigation check the personal biases of scientists.
Thomas Kuhn pointed out that scientists tend to be conservative; they do patch up the reigning theory until anomalies in the evidence become overwhelming and we have a paradigm shift. So there's likely a social dimension of scientific institutions, but scientific methods of inquiry nevertheless filter out dubious hypotheses.
You say the Big Bang theory is obviously flawed. If it were, that would be quite an indictment, since it would imply that the sociology matters more now than the power of scientific methods.