I understand, that is how the badger game works. So you are being conned, and you are innocent. You absolutely right to move with care. No need to rush, this blackmail scam is not going away. Do you have any friends who are lawyers you can consult with about problem like this? Or maybe find a way to get the outline of the story to a newspaper or TV station? A tip about an on-going criminal enterprise? Think about it, maybe you can come up with a way to get the story out, and keep your name out of it. Maybe there is something about this on the web? I googled underage child scam shakedown and saw what looks like resources for guys who are being tricked and trapped.
From what I have read on this site, this is not exactly an unknown problem to police. It is really just the new age version of a very, very old scam. There is a consistency to the reports, SC is the most common. I have seen GA, TN and WV mentioned, but SC is the leader by far on this site. And POF is far and away the most common of the sites involved. This is a big money deal here, and it seems, easy pickin's. I am in the deep South, but it has not hit this area that I can tell, but I am in a very small town, and I think this scam does better in a medium sized city. Not much money blackmailing poor folks.
Yes, it's a scam. A long-running one. There is no underaged girl involved. The parties trying to scam you are adults. Go to police and make a report of attempted extortion. NOW!