Are you kidding? AMEX would be more than happy if you called them up and told them that you'd like to pay them $450 a year instead of $125 a year for a charge card. Call them up.
I called customer service but was told that I need to wait for 13months. Thank you for your advice.
You could always just apply for Platinum and close the Gold card account (or keep it-whatever floats your boat).
You can get an upgrade in less than 13 months. I did just last year. Started with a Gold card on 7/30/2012. Received an email offer to upgrade to Platinum on 12/26/2012 and I followed the link. No issues and no HP I was upgraded and my account was transferred to my new card. Received card on 12/28/2012 in fancy box. Also received 25K points for first purchase with new card.
I always ignored those pop up upgrade offers. If they want you to upgrade they will let you know.