Use American Express gift card on Amazon

EDIT for Dec 2023 and beyond:
Trying to do an Amazon Reload for the entire amount minus $0.10 got rejected every time, even using lower increments like $100 or $50.

It appears you can process two $25.00 Amazon Reloads in a 24-hour period.  You must run one and wait for it to get to completion (takes around 5 minutes), then try the next one.

A better idea (kudos to my boss for suggesting it) is to take your AMEX gift card to Walmart and purchase an Amazon Gift Card from them for the same amount.  Then you can run one Amazon Reload transaction for the full amount.