“overall reputation for leniencies, sometimes lack of transparency, and, OMG, seemingly lack of cooperation and piety towards other authorities…”
Maybe it was a typo but are you aware that your choosing to put OMG in there expresses the idea that this is just drama? That leniences, and lack of transparency are somehow not actually real serious kashrus issue but rather just someone being “over the top”?
It lines up with your, ” so what if you don’t trust them, do you have specifics” attitude as well. A person who doesn’t earn your trust should not be left in a position that relies on trustworthiness