I've only been successful in getting the annual fee comp'd, but that's based on my spend.

No way will Amex waive or move the fee by a month. Having just completed another Amex form for a new card, it does say that it will be billed at the end of the first month's statement -so this should have been presented to you. CS will always get things wrong so whatever is in writing is normally correct.

Assuming UK, is the £300 really a problem?