I don't know about the 31 days. Neither did I take the exam nor cancel it. It was out of my control so I'm hoping they will reschedule me within this month.
Also, I don't understand why we can't personally change the country of citizenship on their website.
Sorry I'm just frustrated.
Sad that you had to go through all this. You are right in accepting that part of it is your fault.
Your best bet is to ask GMAC to reschedule the test. I think they would consider your request if you have enough evidence (email you sent + documents/passport). We've seen people get $250 refunded, so that should be no big deal. I'm not sure if they will do so (reschedule) within 31 days. So your summer plans might take a hit.
Anyhow, stay calm and good luck with the call.