ICUR from New Jersey and Connecticut, so you are probably within 100 miles of this hotel. If a credit card purchase is made in your home state (regardless of distance) or within 100 miles of your current billing address (regardless of state), you can make the credit card issuer "stand in the shoes" of the merchant if you are not satisfied with the quality of goods or services (as long as the amount is > $50). This means you can take the same legal action against the card issuer that you can against the seller (which would depend on state law), if you have made a "good faith effort" to resolve the dispute with the seller (which it sounds as if you have done).
So, if you can't resolve this as a billing error for some reason, you might try beating the credit card company over the head with this provision of the Fair Credit Billing Act. I would say that never having actually stayed at the place would render the service rather unsatisfactory. BTW, there is no requirement to wait for the statement if you go this route. I have had to resort to this twice and in both instances the credit card company put the charge back onto the merchant. Once that happens, the merchant has to sue YOU if they want to try to collect.
See
www.ftc.gov/bcp/conline/pubs/credit/fcb.htm
However, based on my experience with Amex, it won't come to that.