Lots to chew, and I wish I had time to engage more deeply, but here's a few quick thoughts. (I'm a tax policy nerd for a US think tank, but views here mine alone).
(1) The tax/econ jargon for the popsicle problem is "leakage" addressed through "border adjustments." A *lot* of work has been done on these issues; see slides 3-5 here! Including work on points that earlier comments have raised, e.g. deciding between broad v narrow goods categories for border adjustments. I recommend this Resources for the Future paper for a general summary of the issues that's not too dense (whether or not you agree with their conclusion that border adjustments aren't worth it). The Congressional Budget Office (non-partisan official US federal budget scorekeeper) also has a fairly accessible piece.
I vaguely remember NZ-specific work on border adjustments too (considering NZ's carbon-intensive exports and the fact that NZ is unlikely to affect global carbon prices unilaterally).
(2) Population aging, growing healthcare costs, and other structural factors mean NZ has a long-term fiscal problem. If new revenues don't help address that issue, it will mean more eventual real cuts in public investments and services. I'm not optimistic that eventual spending-side changes will fall on those who can most easily bear them. So I'd look to carbon taxes for new revenues (with some of the revenue used to protect low-income consumers) rather than to pay for cutting GST.
(3) If instead of a tax switch, a carbon tax is used as a new revenue source, there's a variety of ways to protect low-income consumers while making sure that price signal reduces carbon consumption, with some revenue left over. This piece by a colleague is written for a US audience, so the detailed delivery of rebates isn't so relevant, but the general discussion about the need to protect low-income consumers is.
(4) If switching GST for a carbon tax, I'd worry about ending up with less revenue and a more regressive tax system. Low-income households tend to spend a larger share of their consumption on energy-intensive necessities (fuel, home heating/cooling) than do high-income households. So I'd expect a carbon tax that generated the same revenue as the GST to be more regressive. On the revenue front, as you note, consumers substituting to "cleaner" goods could have a big impact on the "static" calculations of potential revenue over time.
For a GST switch to be a revenue wash and not increase the tax burden on low-income consumers, the carbon tax rate might therefore have to be set to generate more initial revenue than the current GST, with the excess being used for rebates or other offsets to prevent low-income households from being made worse off by the switch.
Also need to consider that low-income households often can't as easily substitute to low-carbon goods/services, as they may be less able to afford upfront costs often associated with doing so (weatherproofing, fuel-efficient vehicles, etc.). For the the carbon-reduction goal, that's the type of of consumption change you want, as you note. Policies to facilitate that transition (and associated cost) also worth thinking about.
(Been lazily saying "carbon" -- but substitute CO2e or GHGs or whatever universe of things you want to capture!)