I have used the following address:
American Express Executive Customer Service
200 Vessey St.
New York, NY 10285

I usually reserve it until I've had to say something like "This is my 15th phone call about this matter."

The two times I remember using it, one time I got a phone call from a very well-informed manager who seemed to genuinely care and helped fix the issue. The other time it simply ended up in arbitration where I got a refund of the amount in question plus $5000. (They had done some pretty eggregious stuff, like me telling them to not delete recordings of calls, and then they deleted them. Litigation often involves at some point a "preservation of records" notice, which in this case they blithely disregarded.)