Best way to prevent credit card fraud?

The past few years, I’ve seen a lot of orders placed using stolen credit card information. I have set the most secure settings with my payment processor (BrainTree) with AVS, CVV and Risk Thresholds. All of the billing information on the order matches 100% and it gets approved by my processor.

These orders will have a different shipping address than the billing address, which is very common in my industry, as most of my customers are traveling. So it wouldn’t be feasible to only ship to approved billing addresses. Unfortunately this leaves room for legitimate looking orders to ship to a different address and I’m guessing the scammers end up reselling the product.

Once the credit card owner eventually finds out, of course they initiate a chargeback process. When I try to dispute the chargeback, there are no applicable reasons for me to select for disputing. The closest one is something along the lines of “Provide proof of delivery to the AVS approved billing address.”. These fraud orders are often over $400, and I by no means have a high volume shop. So a few of these can really hurt financially! I’ve had 6 so far in the past month.

Also in the past, I’ve tried to submit these kinds of things to law enforcement where the orders were shipped, as well as my own local law enforcement, and of course I basically get the response “There is nothing we can do.”. So these scammers can easily continue to get away with this.

My questions:
1.) What can I do to prevent these types of orders from coming in?
2.) When one of these orders slip through the cracks and gets shipped out, how can I fight it? Or can I? It’s not the merchant’s fault the cardholder had their information taken.

Thanks in advance for any help or feedback!