The owners are recorded when the LLCs are filed with the secretary of state, however these states are simply willing to keep the identities of the owners private
How hackable/social engineering proof are these state agencies? How likely is it that they are already compromised by people acting as resources for federal and non-governmental organizations?
They're just regular departments of their respective states. That is to say, probably about average susceptibility to hacking and social engineering. I don't know any specifics about what might be sent to the feds, but you can be damn sure if the IRS or any other federal agency calls the state they will fully cooperate. None of this would actually work to hide from the government, just from random non-expert members of the public.