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.
I did, a lot. I spent a full month, so I could see everything from Auckland to Invercargill. In America we get a distorted impression of NZ as some sort of leftist satrapy. Just as in this country, this is because the news media are run by a small clique of self-absorbed urban liberals. Notice that the editorials in Scoop are mostly written by foreign leftists, including some America-hating Americans I've never heard of (who in hell is Daniel Patrick Welch, for example?). But out in the rural "red provinces", farmers don't own any newspapers that are read interbationally. You need to do more blogging. That's how we get around them.