They don't have enough. They have some conjecture and some contracts for land deals. They don't have enough (yet) to really show a conspiracy. Even if they went to the media, the conspirators are highly connected. Nothing would come of it.
They had enough on them to send real cops go after McAdams and alert the media to her situation, and even kill a state attorney. If the documents and whatever evidence they have on Caspere's murder, or the eco disasters they caused, or even the original diamond theft and murder is brought to light, the conspirators will scatter like roaches, and their power would be diminished. If they hadn't put out the APB then the detectives wouldn't have to play that card yet. Seems like the conspirators had lots of options between where they were at and what they did.
Unless those contracts are worth actual money and not just a paper trail. It seems like the money is more important than dealing with the law.