I'd alert the credit card company that you are pursuing this legally, then I'd take all of the evidence you've described and contact the FBI and your police department. I don't know if there would be any possibilty of mail fraud/interstate line charges (I don't know much about this stuff) -- but I would want this guy (assuming it's a guy) prosecuted to the fullest extent and to suffer as much as possible (having been a victim of theft, fraudulent charges, ID theft, etc. before, I'd be out for blood).
I'd also contact the state attorney general in the state where the credit card originates and perhaps where the purchase is made. I'd just pursue everything.
This seems like such a no-brainer. I'd go to the FBI for sure -- they do have an ID theft division:
Since it involves interstate commerce and mail (or UPS or whatever),and the internet, there could be several crimees here. But check with local law enforcement too. Clearly there's a lot more here than simply getting the charges removed from your credit card -- though of course that's clearly your priority.
Copy all documentation sent to law enforcement to the credit card company, too (and your complaint to the SAG). Years ago, I complained to the SAG and that was enough to remove charges on one of my accounts (an internet vendor that never delivered). Since this is a large amount, you may need to threaten (and pursue) legal action with them.
If you show that you are pursuing this legally, you should get your refund. And I would think that if you press charges against this creep, he would not only face prosecution but restitution. (I'd be after his house! Yes, I am vindictive and obviously still furious over our burglary!).
Another thing: contact each of the credit agencies (Experian, etc.) and tell them you've been a victim of identity theft. They will put your name (or DH's, or both) on a list where -- if any attempts to change your information are made -- you will need to be notified first at the phone number/address you choose. When our house was robbed years ago, I put the names and SS#s of me, DH and DD on this list, and I updated every three months. I just stopped doing this a year or so ago. This should ensure that no one else is able to tamper with any of your accounts (credit, utilities, etc.).
I hope some of this helps. I definitely wouldn't fail to pursue this with authorities. This guy will just keep doing it unless he's stopped, and I think he should have to repay you not only what he stole, but something for your inconvenience and anxiety.
GL and keep us posted.