Hainan Airlines AKL to LHR (via HAK and CSX)

Jim, you are a New Zealand citizen. You really do not have to bother yourself about all those visa free transit stuff. You are allowed to transit, stay and explore entire China for up to 15 days absolutely visa free.

So, on the plane that will take you to Haikou, you will take one arrival card and fill it out. You should just tick the box - transit.

Upon landing, go straight to the immigration with your passport and the filled out arrival card. You will formally enter China since your next flight segment will be a domestic one.

Why you arrive in Changsha, you will cross the immigration to formally exit China and just head to your gate for your flight to London. Fairly easy, as you can see... By the way, if you were not form a country that does not need a visa to enter China, such an itinerary would be eligible for 24 hour visa free transit without any doubt. Have a nice journey.