Iphone repair outside of country of purchase

Hi everyone, I'm really hoping someone can help me.

I was on holiday in America back in June and my camera on my iphone 4s stopped working. Because of this I purchased a brand new iphone 5s from the Chicago Apple store.

Less than 3 months later there is an issue with the Bluetooth phone connection. My 5s will connect to any Bluetooth device but if someone rings me or I ring somebody there is no sound. The Bluetooth audio streaming works absolutely fine with no issues. I have spoken to Apple Support numerous times and they agree it must be a hardware issue and to send it in for repair. This is where my real problem begins....

I live in New Zealand where we do not have an Apple Store that I can either take or send my phone to. Apple Support have told me that my only option is to take my phone in to an Apple Store in either Australia or America and that there is no other option. I cannot simply send my phone to any Apple service provider, I have to take it or have somebody else take it. I don't have anybody in Australia or America that can do this for me.

Please please help, there has to be some type of option available to me. I have spent USD$800 on an iphone that has an issue and because I don't live in the country where I bought it from or Apple has a store no one will help me.

Any advice would be much appreciated.