I now KNOW that a NZ Tivo will NOT work in Australia.
Tivo's reasoning is that a unit must be repaired in the country of purchase, and if they allow transfers across the Tasman then customers will expect local support. This would cause many headaches for Tivo.
Having said that, "Good Guy Tivo Australia" took pity on me and added my NZ-serial-numbered-Tivo" to the Australian pool. Thank you Tivo Australia.
I was told that this was a one-off and since I am now aware of the rules, it won't be done again.