I'd start with doing a full chargeback for all months, and provide as much documentation.
Additionally, I'd reach out to folks like Ars Technica, after ensuring such an issue was not a result of my own error.
One big red flag with this story is that OP seemingly did not notice $1,500/mo coming out of his account. That is most certainly something that anyone would have noticed, even someone making a few million a year, and if you make that much money, you definitely are paying an accountant to manage your accounts.
The story smells off.
EDIT: Oh and I'm not denying that customer support at AWS and other places has gone way downhill which IS a problem, however, there is no way this story is realistically true. At the very least, the numbers were inflated in order to draw in attention. No normal person overlooks an additional $1,500+ per month bill on their bank statement. Even small businesses would've been all over that. I know, I've worked for and managed them, along with being a senior software engineer and manager.
Many states have codified tort laws as being in the interest of public policy (e.g. most consumer protection acts). If this person were to sue under such a statute, it allows courts discretion in nullifying clauses like this arbitration clause.