UPDATE: Seems that they do read their emails, as I received the following response from CoinTerra within minutes of notifying them of the actions I had taken:
Agent Zero (CoinTerra)
Apr 23 09:31
Hello REDACTED,
I have just been assigned your support ticket. Per your request I have canceled your order for your June delivery GSX-I card and forwarded your refund request to the finance department for processing.
Regards,
CoinTerra Support