Thanks for the response!
I'll clarify; I have no problem accessing the TVNZ website. The problem is the playback of actual content that's blocked when attempted access through the New Zealand server. I use a login, which works fine, but when the player loads, it brings up the same error overlay as in the image in my original post.
https://www.tvnz.co.nz/shows/the-dry/episodes/s1-e1
Here's a specific Amazon URL:
https://www.amazon.com/gp/video/detail/B07VVFSR7G/ref=atv_dp_season_select_s2?jic=36|CgtmcmVld2l0aGFkcxIMc3Vic2NyaXB0aW9u
That's through the Chicago server (which I arbitrarily favour as a US server), but none of the other US servers make a difference, nor does a private browser, or deletion of internet data.