Unless the contact with Amex Travel is mandated or necessary, you should absolutely avoid their human agents. They are not exactly competent, and have many pages of history of mangling even idiot-proof tasks. It's also unwise to proceed blindly when you can see all your options on the screen in front of you.
Adding a 2nd person directly with the hotel can be done by any means. But always follow up with a written confirmation (e.g. by email or fax).