Hi Peter,
I've had a bash at different things, and we have a winner:
https://www.smartdnsproxy.com
I used the 2 week free trial of the above DNS solution, and followed their directions. I then changed the PC's timezone to Auckland, NZ.
Opened up:
https://www.tvnz.co.nz/shows/hillary/episodes/s2014-e4
Signed up for an account. I used the URL token, rather than the email link (2nd option). Videos now play without a fuss. 2 weeks trial should be enough to get through the series. As a bonus, my Wife's Japanese Amazon Prime Video is now viewable here too.
Remember in the SmartDNS settings to change your "Channel B" country to "new Zealand". This is where TVNZ is categorised in SmartDNS.
See pic below for proof - Happy watching
