I think the first thing is that this was not a fraudulent charge but more of a "service not provided" situation.
I wonder if the mis-classification resulted in some part to your unfavorable ruling by AMEX.

Second, with these kinds of cases credit card companies do expect you to do a little bit of leg work before you file a dispute. So put together a follow up packet with
- confirmation email that you booked with the OTA
- a letter from the hotel that you demanded that they fulfill their obligation to house you, but that they did not, and, the reason, in this case - they had no record or explicit obligation to provide any service to you according to their systems. You can either attempt to get this from the local hotel itself or the corporate customer service for the chain.
- declaration of attempt(s) to resolve the matter with the OTA directly - letter, emails, or list of phone calls that you made to the OTA to get your money back and resolve it directly with them that were unsuccessful.

With all of that, then AMEX should rule in your favor and withhold the release of future funds to the OTA and it will be up to the OTA to prove their case to get the funds released. I'm speculating but perhaps the initial AMEX person simply had to adjudicate whether this was fraudulent or legitimate because of the classification - and technically it was a legitimate charge - but service was not provided.