I've largely avoided responding to specific questions because I don't want to take this thread further off topic. I'd only shared part of the story about why I am pursuing a claim against a former model so as to frame the questions I was asking about how to make contact, a necessary part of the legal process, in the least harmful manner. It's understandable that both scamming and stalking are hot button issues for many people on both sides of the fence and that some people would be inclined to fill the gaps I've left in my story based on their own assumptions, but I don't want to get tied up in a debate about those issues and continue bumping the thread.
There is no good way for you specifically and personally to contact her. Any direct contact between you and her is hella creepy if she hasn't given you both that information and permission to directly contact her.
What you need to do is hire an investigator and eventually a lawyer. The investigator to find her; and the lawyer to be your middle-man for all communications. You are never going to talk to her directly; your lawyer will be your soul eyes, ears, and mouth. You get the lawyer to write a letter laying out your claim, what you want or need, and how she can remedy the situation. And a month or two later when she most likely hasn't responded, you send a lawsuit thru a second lawyer (found by your first lawyer in whatever jurisdiction she's really in) who then serves notice in her local court system that she's being sued for $1000 dollars. You and/or your lawyers are going to have to show up in her local court and run the case for a day, a couple of days. If you're really lucky you'll get your $1k back and then your lawyers are going to take it and about $20k more for their time and services.
If you want to burn your chances of getting any service on any cam site, you can petition the cam site for restitution of your lost funds; however you've been a fucking dumbass and waited until they paid her. You're shit out of luck; you don't pass go, you don't collect $1k. What you do get is banned, your cc banned, your email banned. She didn't scam you, you gave her a gift.
Or what you really should do is suck it the fuck up. Accept that you got taken and are probably never going to get your money back. You took a risk, you sent an anonymous individual, whom you erroneously trusted, a large sum of money and expected to get something without any degree of security or reassurances. You fucking idiot. You should have required assurances, insurance, or proof of faith: like a verified phone number, or email. Don't send anybody any large sums of money without some degree of protection, or a means of pre-approved contact to resolve conflicts that both parties agreed to: if you had an email or number she gave you, then you might call her up and ask what's going on. Barring that, it would be a place for a lawyer or police to start looking into things.
Take precautions and don't let your dick do all the thinking