I thought the J1/J2 visa for the US ended a while back but I can imagine it continuing.
It is a flawed system having instructors that were recent grads but it is the system nontheless and places like Canada that have generally experienced instructors are very difficult to places find work afterwards.
Either way in the US if you can get some hours as an instructor and follow the well trodden path to the tour market or the GOM or the many medevac jobs then you may get your first 1000 hours faster than in NZ.
Your past work experience is key to your first job as a new pilot.
That may open the door to Canada which is easier to immigrate to than NZ or the US and depending on which school you choose may have better training.
Make your choice on where you can work as a new pilot or else you may have simply chosen a very expensive holiday.