I found the answer - the advice from Amex online chat was incorrect. The merchant code for failure to provide a service is as follows:
REASON CODE 4553
Not As Described Or Defective Merchandise
Chargeback Reason
Maximum time a dispute can be raised
Maximum time to challenge a dispute
Excluded Transactions
Requirements to challenge a dispute
Either of the following reasons:
1. Card Member received goods and or services that are different than
the written description provided by the Merchant at the time of purchase.
2. Card Member received damaged or defective goods and or services.
One hundred and twenty (120) days from the date American Express Network processed the Transaction, or
One hundred and twenty (120) days from the date the goods and/or services were received.
Twenty (20) days from the date of Chargeback. None.
One of the following items must be provided:
° Proof that a correcting Transaction, which directly offsets the disputed Transaction, has already been processed (Reason 1, 2).
° Proof that refutes the Card Member’s claim that the goods were returned, or services were cancelled (Reason 1, 2).
° Proof that refutes the Card Member’s claim that the quality of the goods or services provided did not match the written description provided by the Merchant at the time of purchase (Reason 1).
° Proof that the Merchant attempted to repair or replace the damaged or defective goods or provide replacement services (Reason 2).
° If the Card Member claims the goods were returned, proof that the Merchant provided its cancellation / return policy to the Card Member at the time
of the purchase, and the Card Member did not comply with the policy,
or applicable laws and regulations (Reason 2).
° Proof that the Card Member agreed to accept the goods or services “as is” (Reason 2).
° Evidence that this Chargeback was raised in error and the disputed Transaction does not qualify under this Chargeback reason (Reason 1, 2).
The Merchant may also submit the following as Compelling Evidence:
° Proof that the goods and or services matched the description provided by the Merchant, e.g. photographs or e-mails (Reason 1).
So if I have no joy with lastminute I will take it up with Amex when I am back in Australia.