My guess is that the FB TOS requires arbitration for all disputes arising out of use of the FB platform, or some such broad language.
Chargebacks are one idea, but it likely won't get you all your money back. I have to imagine that FBers on HN could connect you with a lawyer there — can you leave a throwaway email account in your post so that people could reach out to you? I'm a nobody but do know a lawyer or two at FB.