The problem, as you have described it, sounds typical of customer service at many mass market organizations. I don't think there is any recipe for obtaining satisfaction because your business is not important enough to warrant individual attention at the level required. I know this isn't what you want to hear, I know American Express would hotly deny it, but this is my conclusion. (To be sure there is no misunderstanding, I think this is the case with every mass market enterprise without exception. It's not specific to American Express.)

If you want to pursue the matter by telephone I would begin each conversation by asking, "Do you have the authority to [insert specific action]?" If the answer is no, ask to speak to the next level. However, my hunch is that the decision would require someone who simply will not speak with you.

If you want to pursue the matter in writing, hire a lawyer to write on your behalf.