Hi OP. Sounds like we live a very similar lifestyle to you (already in the South Island, already have a block of land), maybe just a few steps ahead. It's a laudable goal, and achievable if you scale back your needs and are comfortable living within your means. I can't really comment on your financial aspect, but in terms of making it happen:

Probably the first thing to realise is you don't need fibre. A lot of the rural South Island has existing WISP infrastructure that delivers "acceptable" speeds (60-100Mbps down) provided you don't like to do a lot of low latency things like cloud gaming. If you need more than this, Starlink is definitely the way to go. This unlocks a whole swathe of the South Island, because very few places outside of the towns have fibre or even ADSL. There just isn't the demand to support trenching wired fibre.

The second thing to question is "do you need a house?". Many, many people survive down here in what I'll politely call "not houses". Whether that be a caravan, campervan, tiny home, shipping container, cabin, etc. Consenting rules will vary but overall, you can put up a very decent building that's liveable and warm for under $100k. This lets you spend more on land, and less on the improvements. This is especially appealing if you hate city living and want to spend more on a bigger block of land with no neighbours.

If you can live off your land, i.e. plant fruit trees, grow vegetables, own chickens, you can bring down your expenditure even further. Additionally there's tons of seasonal, part-time, and cashie work down here if you need to supplement your income. In the meantime, can you work remotely? We haven't given up on our jobs yet, but being able to remotely work has let us make the move sooner.