Maybe like Crystal Films... just kidding. Some of that is a little too serious. Maybe something about the speed of virasaptfights or something similar. Definitely no "pillow fight giggling".
I hate to say this, but you are looking at about $300 to do something like this on your own (150 per fighter).
You are lucky that you live in Atlanta, though. I would contact Catfight Haven or Vira's Apartment fights to see how much it would cost for you to sponsor a fight that you could attend. They might not even have this as an option, but it could not hurt to ask.
Your biggest hurdle doing this by yourself is getting women to believe you to show up to do this. Right now you have no cred as a producer to do this, even though you do not want to film this.
You could also sort of be a manager to women looking to do competitive catfighting. The Haven and Vira are always looking for good local women to use as fighters. Recruit someone at a strip club, craigslist, a real life friend, fetlife to work for them, and you could be an escort. That would be free for you.
It's hard, but best of luck. The biggest advantage you have right now is being around Atlanta.