HS what you have observed on this forum is that there are basically two distinctly different types of hunting in New Zealand and although it is a generalisation and not entirely correct to do so, you could group them in to short range hunting (which is predominent in the North Island where the hunting areas are mostly forested) and long range hunting (which is predominent in the South Island which is alpine). 30-06 would be fine for NZ. In my view your Zeiss would be over powered for bush hunting and would likely be underpowered for truly long range, however I will defer to other members to give you guidance on that.
In the end, a good comfortable (to you) rifle that will cleanly kill the animals you mentioned in Europe, will also cleanly kill the same animals in New Zealand so go with your gut on this.
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