I'm only reporting what I saw. Though Kiwis served honorably in WW II, especially as they saw the Japanese asland-hoppiong advance pushing toward them, the WW I esperience seems to have meant much more to the national spirit. Why else would every little town have a WW I memorial, while in a month I saw precisely one WW II memorial (dedicated to the USMC deployment to Guadalcanal, which trained near Wellington). A succession of films like "Chunuk Bair" carry the same theme.
I asked New Zealanders in different walks of life about this. The consensus seems to be that WW I represented the nation's first big break with Britain. Before that, NZ had faithfully sent troops to battle whomever Queen Victoria had designated as the fuzzy-wuzzies of the moment.
The second big break with Britain came in the early Sixties, when Britain joined the EU and the farm quotas it imposed on all countries not part of the great socialist experiment. NZ suddenly found itself out in the cold, abandoned by the Old Country. At that point, NZ decided to rebrand itself as a Pacific nation.
So why is most NZ lamb sold to the Arab world today? Nothing ideological is involved; despite high US consumer demand, the American farm lobby imposes stiff quotas on NZ agriculture. When socialists can't compete in the open market, they get the government to 'fix' things.
I hope you enjoyed your trip here. But you didn't look hard enough at the memorials. They are indeed covered with the names of the young men who died in WW1. The small farming town I grew up in has one on a hilltop - the names are those of the families who still live in the district. Although it was built after WW1, on the other side you'll find the names of those who fell in WW2. And on some of the memorials you'll find sections for those who fell in Malaya, Korea and Vietnam. They are more than just WW1 memorials.
"Chunuk Bair" was filmed not too far from where I live. The Aussies have a film called "Gallipoli" that's better done, but on a similar theme.
Just to correct a couple of points. Before WW1, NZ sent troops to one British war: the Boer War. The "fuzzy-wuzzies" we were fighting were Afrikaaners - South Africans of Dutch descent. We were still sending troops to fight alongside the British as late as the Malaya emergency in the 1950s.
Even after WW1, NZ was most reluctant to sever links with Britain. The Brits passed a law in 1931 that allowed NZ to claim full independence. NZ refused to ratify it till 1947! I wish I could say we were keener to grasp our independence, but we weren't. So the Kiwis you talked to might have led you astray a bit.
Britain joined the EEC - which became the EU - in 1973. I agree - that was a real psychological shock to NZ, even though we'd had warning.
And most NZ lamb is in fact sold to Europe, despite quotas and tariffs. We'd love it if the major Western countries joined little ol' NZ in dropping most trade barriers - letting us earn all the money we work for - but we're not holding our collective breaths on that. NZ used to be a heavily-regulated, Socialist-style economy. That failed. We're now doing far better after free-market reforms. Even the bunch of loopy lefties in government at the moment don't dare change the economy back to what it used to be. Agricultural reform works. It was hard on our farmers at first, and it's still hard work for them, but they're now successful at growing and raising things that foreigners want to buy.