Better yet, why not purchase American Express Gift Cards through Big Crumbs? You will get cashback and the card processing fee is waived if you use code EMSVCA.
You will get 1.6% cash back, so the cost of those 16,500 miles would be $300 - $240 Cash Back or $60.
That's a Cost Per Mile of 0.36 cents - which is FANTASTIC!
If you do go the American Express Gift Card Route, make sure to buy the cards from the Business section of the AMEX gift card website - the personal site has a limit of $5000 per purchase.