Ah, I would overpay. Only a few creditors frown on that and I don't think AMEX is one of them. I would go with the CSR on this one.
+1 If you overpay by the exact amount of the annual fee then you'll be set.. Some creditors DO frown upon overpaying because then they usually have to mail you out a check or make a credit to your statement etc.. Also, somebody else mentioned that if this gives you 0 util then Fico will ding you..Im not sure if this is true or not but i would be interested in finding out the answer.. Does your score get penalized for having a util % and then dropping that % to zero?