I recently submitted a support ticket and got the following response:
Quote Originally Posted by <support_na_ig2@square-enix.com>
Hello and thank you for your GM call. Unfortunately, the matter you have reported cannot be addressed through an email with the information provided. For assistance, please contact a Game Master in-game, and we will work to provide you with the best possible resolution. Thank you for your patience, and best wishes to you.
FINAL FANTASY XIV Game Master Team
How does one contact a GM in game? I have navigated the Support Desk menus in-game and nothing seems readily obvious as to how to actually do this.

A sad moggie is sad.