If you are going to asia, some of the Chinese travel agents who offer dicounts in business class may be able to offer you a "C" class fare.
The ticket would show "J" as the fare basis, but "C" as the booking class.
Also, the "J" fare would be printed on the fare box of the ticket.
(There would be additional restrictions printed on them like "NON END, REFUND TO ISSUING OFFICE ONLY" etc.)
Whether you can use this kind of ticket with the AMEX promotions depends on whether if the issued ticket has a "tour code" printed in the "tour code" box of the airline ticket.
Only one tour code is allowed on the ticket (so make sure if the AMEX fare requires tour codes to be used)