Sucks to say it but having to double-pay this invoice may still be a better scenario than having the business fully banned from Meta Ads.
I'm not an expert on finances at all, but I'd pay using the old method, then chargeback. If they then cancel your account, they'd have to repay the new payment too, and I think someone there would start wondering why the hell they're cancelling you then.
I get that there’s a real risk here that you could wind up out another $40k at the end of the day and your problem still isn’t solved, but if losing access to the Meta market is as fundamental a risk to the business as I took away from the post, then it seems to me like job one is to ensure that the business survives and that the (admittedly unpleasant) process of getting trued-up on the $40k is exactly the kind of thing that your lawyer is for.
(source: patio11 has mentioned more than once holding a handful of shares in companies he's a customer of to make him eligible to use that approach)