Im a New Zealander, and can give you help if you need it. And showing how randomly small the world is, Ozy Clint and I bumped into each other one day in the bush.
So issues at the moment are number 1, our Govt is not letting in any tourists due to the Covid thing. That will change at some point, but best guess would be 12 months or more.
And two, if you are set on a Tahr hunt, then you should know the Crazy green govt we have here is actively involved right now in exterminating all Tahr from much of their territory. Including the areas In Clints report. I dont think they will get them all, but it is going to become a low percentage success hunt. One that was all ready hard enough.
There are lots of places to hunt other game though. If you are after alpine animals I would consider Chamois as a fantastic hunt. Or red deer. But do not expect to see the massive trophies marketed to American hunters. They are not representative of reality. Yes we have plenty of wild pigs- similar breeding to much of what I see on here from the states. Wild goat, fallow deer plus a few others.