Totally not an answer to your question, but for the extremely rare cases I choose to watch TVNZ+/ThreeNow, I use their KODI plug-ins (Would work on SmartVU un-sure if on Fire Stick).
UI is obviously not as nice, but 0 adverts and it works amazingly well. 

I run PiHole at home, and I am unsure if this is also helping prevent adverts. 

Amazon are now blocking third party apps on their Fire Sticks.

Dish TV's sticks are quite slow.

Would recommend the Google TV steamer or even an Apple TV (assuming you've got iPhones).

To confirm your other question - NextDNS / DNS blocking doesn't break ads in either of these apps.