Just to clarify.
You can operate in the SIM only without a Class 1 Medical in both jurisdictions. You can also obtain a CAA NZ Flight Examiner approval without the Class 1 but I'd have to double check the OZ requirement (I believe it's the same).
The biggest issue is that both CASA and CAA NZ will not recognised the fact you have been or currently are an examiner outside of their systems. This will mean you will need to convert your licence and then jump through the hoops of obtaining the required instructor rating (D Cat or FIR) before moving onto the FER qualification. Finding somebody to do this process given the time and expense of doing it in the SIM, it's highly unikely you will find an organisation capable of delivering what you are after.
Sorry, probably not what you wanted to hear
newcrew