Another part of this: the spread of globalisation coupled with the UK's history of colonial expansion and the availability of cheap fuel are the main factors that even made it possible for you to consider moving to NZ in the first place. I would say you have no personal responsibility for those phenomena, all of which were already in motion well before you were born. Can you and millions of others be blamed for taking advantage of this situation to move and try to improve your circumstances? I don't think so. The difference is that previously long distance migration of this kind was a one-way ticket and people knew they were likely leaving the land of their birth for good and would have to create lives for themselves from scratch. Cheap air travel now makes jetting back forth possible, and thus makes the decision to migrate less final.
The problem of 'love miles' in the context of climate change is a difficult one. Eventually the rising costs of fuel will 'solve' the issue and make the world bigger again, but that won't comfort the people separated from their families, or from their new lives if they decide to move back while they still can.
From the point of view of personal responsibility over ghg emissions I generally don't agree with individuals taking that upon themselves when it's the system that is to blame, but that's harder to argue with actions that aren't strictly necessary (though travel for family is more justified IMO than travel for tourism). Maybe consider the concept of leverage in setting up your own personal 'off set'. Consumer decisions are relatively low leverage in the overall effect they have. Voting is maybe a little higher, or writing to your MP, signing petitions. Legal work or lobbying somewhat higher, and so on up the scale through protest, direct action, strikes, revolutionary activity etc. You could decide what an appropriate action or series of actions might act to counterbalance the effect of your flights. It's better than paying some company to plant a tree which will probably die anyway!
No real solutions to the predicament unfortunately. It's something I struggle with too with lots of family in Europe. Haven't flown since 2019, and now I'm self-employed the long train/bus journeys are slightly more feasible, though much more expensive... We do what we can.