The basic premise in the 1950s/1960s is that the Labour government under Nash never collapses in the 1960 elections, but virtue of there never being a "Black Budget." In general, the post-war consensus of Attlee & Co. remains strong across not only the United Kingdom but the Commonwealth as well. The economies of OFC during this period are slightly more advanced and wealthier than OTL, giving the Labour Government less of a gap in spending to plug. New Zealand's export market was very strong, still exporting to Britain and the Commonwealth on a very favourable basis. While there is still a need to increase some taxes, it was just seen as another run of the mill increase, coupled with the popular increases in social security benefits.
This allowed Labour to win the 1960 election by a small amount, and Nash continued as Prime Minister. Holyoake would still go on to win the 1963 election, but he would only win it by a few seats, leaving the two roughly evenly matched in the House. Holyoake would continue on in 1966 election, but would lose in 1969 to Nordmeyer. Known for his religious views, he couched accepting the African diaspora (in the late 1960s, this was limited to the White African diaspora) in religious terms and to provide for the social welfare of all people. With the door opened, this eventually led to the acceptance of Black Africans in the 1970s at the urging of the British. It is also worth noting that the Commonwealth Constitution, of which New Zealand was party to in the 1960s, allowed for relatively open inter-Empire immigration.
MMP was introduced much in a similar way in New Zealand. While there was no Thatcher or Reagan, there were similar politicians who pledged to smash the old order (again, of Attlee & Co.) who came along and brought a giant hammer to the delicate economies of many western countries. What resulted was a pretty dramatic falling off the cliff for a bunch of countries as they saw deficits explode, and everyone run around with more money in their pockets, but suddenly less services. MMP comes around during this time period when everyone has nothing but contempt in their hearts for the people who decided to fireball their economies.
The best way to understand why Commonwealth countries have low income inequality is because they represent the "middle" Superpower between the left-Communist of the Soviet Union and the right-Liberalism of the United States. They pride income equality, services to the poor and downtrodden, as well as high taxes on higher earners, but also creating an environment where high earners can flourish.
I will re-work the numbers on the Maori population, they should be about the same as OTL. I think some wires got crossed in my spreadsheet. Watch out for an update on that part. As for the African population, there's roughly 15-25 million people from southern Africa who are refugees in either other African nations or outside of Africa alone. Tiny New Zealand garnered a bunch of them.
Edit: It's been fixed. The 'exact' breakdown is below:
3,257,602 European
753,485 Maori
439,174 African (incl. White & mixed)
156,784 (Other)
I'm glad the irony isn't lost on anyone else.
Dave's redistricting when it works (it often doesn't), but I have a map of every town and city in New England (linked elsewhere), and I have the population of each municipality. I just mix and match until I get the right number. OTL Atlantic Canada I have a special formula for.