A word of caution. Credit card companies only allow you to challenge a charge within 60 days after the charge is posted. We recently bought tickets in July for travel in December. Air Malta denied us boarding even though they created the problem. AmEx was unable to cancel or challenge the charge because the charge was more than 60 days before the problem happened. Very few options to solve the problem remain, apparently.
Just to clarify - federal rules are that the 60-day limit starts the day the first incorrect bill was mailed to you, not 60 days after the charge was posted. Not that that will help your situation.
Make an argument for fraud. Fraudulent inducement to purchase, failure to delivery goods, contract performance. There is no time limit on claims of fraud.