The hours you log should count no matter what. Just that as mentioned earlier, Taiwan CAA ratings are not ICAO so therefore, are not guaranteed to convert. The ex-EVAs hired by Emirates/Korean Air/mainland Chinese carriers most likely had their employers facilitate or sponsor the conversion process.
I've heard that some countries which have better relations w/ Taiwan will allow conversion via an informal arrangement. It's probably best you specifically confirm w/ NZCAA though to see if they have such an process.
We did have a Kiwi Taiwanese at our flight school who made it to CAL. Good luck!