Well c'mon, in this case I think OP has a legitimate gripe. If the charge doesn't get credited back in short order, it sounds like OP will have to either shell out cash to avoid interest charges/late fees on his/her card bill or...incur interest charges or late fees on his/her card bill. And before we all go accusing OP of not planning ahead to avoid this situation, I find it quite easy to imagine a situation where one might end up cancelling on such a time frame. The problem from the consumer standpoint is that CX's delay in processing the refund causes a cash-flow problem on the consumer's side.

OP, I've never been in this situation myself, but perhaps a call to Amex to explain the situation would result in some help from their end? I've found them to be quite accommodating in other respects over the years. (Including one case where they waived a massive interest charge that had racked up because I had mistakenly paid HKD120 short of my full balance one month and then got walloped with interest on the entire monthly balance of HKD20,000.)