Massive fraud/spam problem

Hey – I’m hoping someone may be able to point me towards a solution here… Here’s some context into what I have going on:

It seems my site has been targeted by a group of people who complete purchases through my website using what I assume to be stolen credit cards, and they always put their shipping address as somewhere in Miami, Florida. They use fake emails that are always different, random names that are sometimes just “aahhhhhhddddjjjj” and things like that. We NEVER ship their orders out, and sometimes they’ll place 10-20 orders within a half hour or so, usually with different names, emails, and Miami addresses used throughout. I’ve tried blocking IP addresses, but it seems very easy for them to use another one to bypass the block. The payments go through, but we always mark the payment with a custom order status of “Suspicious Payment” and refund the payment source. When I track the IP address it’s from places all over the world – Thailand, South America, other random countries, when I sell men’s and women’s yoga clothing and activewear inside the US. It’s very easy to tell that these are spam/fraud orders, but they’re real people putting them through.

How can I put a stop to this!!! I’m sick of it and it’s really getting out of hand. I’ve installed plugins to monitor the problem but haven’t found a solution to actually STOP them from coming through. I can’t blacklist emails or addresses because they’re always new and fake and they tweak single letters, etc to bypass. Is there any way to permanently block this type of order from going through?! All help is appreciated.

Thanks for your time.