Response I just got after sending a support email:

"Hello and thank you for contacting the GM team. We understand you were unable to change your character's appearance and apologize for any inconvenience this has caused you. While we cannot guarantee that your character's appearance can be reset, we have taken the information you submitted and escalated it to the appropriate parties.

Thank you for your patience and best wishes to you,
FINAL FANTASY XIV GM Team"

Eh... I was pretty specific about wanting a full reset to change my class/starting city, as well. So this was probably an auto-response. But it's cool they responded and escalated it. Edit: Oh, also, this was a million times faster than getting any sort of support in FFXI. So also cool.