winksmith, I sent you a PM. As for furthering the discussion of a potential problem I see, you will need to find an FAA certified pilot, and potentially a N registered aircraft. I am not sure given the way the rules are worded that you could take a FAA CFI, who has NZ CAA licensing, and fly a ZK tail aircraft. That would be a question for a FSDO in the USA, or the CAA in NZ:
"Can an FAA flight instructor administer a FAA BFR in a foreign registered aircraft, if the flight instructor also holds licensing in that country?" If the answer is yes, there will likely be some sort of exemption, if the answer is no, you will have to find someone with a N12345 in NZ or Oz, or take a trip to Hawaii, Guam etc where you can find an N registered aeroplane.