People use the term "embassy" and "consulate" interchangably. The key is to know what services are available and where.
It may even be that Amex won't insist on a US notary.
As to the SSN, I am not sure what OP means. Does Amex want his physical card or the number. If the latter, doesn't he know it or can't he call someone such as an employer who might. Getting past this incident, having that number handy can be important for a broad range of things.