The logistics that are required to mount an opposed invasion of nz is a deterrent on it's own if there is the ability to oppose an attempt. This is not the case at present. The 2000km moat is the first line of defence and while interdicting trade routes etc will cause a significant amount of grief, it will not result in the loss of our freedom and sovereignty. My opinion is that the preservation of the sovereignty of a country is the first requirement because if you lose it everything goes.
In NZ's case being able to contest the air and sea of the said moat is a powerful deterrent, This is something we can't do at present.
IMO in order for there to be a preservation of sovereignty, some ability to maintain and protect vital SLOC is also required. The fuel issue in NZ is a looming, albeit IMO rather silent problem facing NZ given the situation in the Mideast. According to reporting from a variety of sources, NZ has roughly a 52-day or 53-day fuel buffer, but some of that reporting also suggests that the quoted number itself has some problems.
NZ basically imports refined petroleum product, having largely or completely stopped refining at Marsden Point AFAIK. The largest refining sources of refined product for NZ are in Singapore, S. Korea and Japan, all of which are reliant upon deliveries of crude oil from the Persian Gulf. Further, being NZ is an importer of refined product as oppose to crude which gets refined in-country, there is a lag between when petroleum in crude form is shipped from the Gulf, to when it gets to NZ as refined product. From the reporting, the NZ petroleum supply chain itself operates on a roughly 52-day cycle which means that the impact of delays or failures/losses in shipping crude from the Gulf will not become immediately apparent. Refined product shipping to NZ typically takes about three weeks to be delivered. This means that petrol and other refined fuels arriving in NZ now or in the next couple of days likely was delivered to the source refineries by the end of February or very early on this month. Going further back with the numbers (yes, for those who have noticed, I have found keeping track of the timing of things can be very important) the product bound for NZ leaving the refineries in Asia likely shipped from the Gulf as crude about a month before would start to get shipped to NZ after being refined and blended. Or put another way, refined product just getting to NZ now likely was part of crude oil shipments from the Gulf which left at the end of January or very beginning of February.
Where this can start being an obvious issue will likely come around mid-April, when crude deliveries to the refineries could drop depending on how much disruption there has been/is with the flow of tankers from the Gulf. If the flow of crude gets reduced or interrupted, there could be less or even nothing for the refineries to process, and then it would about three weeks after that where NZ might really start to see increases in fuel costs and/or fuel shortages.
OTOH, it is also possible that the gov'ts of S. Korea, Singapore and/or Japan could order the refineries to not release product for shipment to NZ if there is enough concern about potential domestic fuel disruptions if the flow of crude oil becomes seriously limited or even stopped altogether.
Now consider the sovereignty question again, but with the security vignette also including limited fuel stocks available across NZ because NZ has only been able to receive on average a small tanker's worth of refined product per week for the last six months, rather than the roughly three small tankers worth of deliveries needed to keep pace with normal NZ fuel consumption. A patient and calculating adversary could then take advantage of NZ fuel deliveries getting cut and wait until NZ might only have a few days worth of fuel before really starting hostilities, leaving the NZDF and NZGov't as a whole with limited mobility and force endurance due to a lack of available fuel. An adversary that also possesses some form of standoff land attack capability could further exacerbate the problem by launching surprise strikes at fuel receiving and storage facilities in NZ, like those at Marsden Point (currently receives some 40% of all NZ fuel imports) as well as a couple of other receiving/storage facilities around the country.
IMO if NZ's fuel stores get so low that the country only between a few days and two weeks of fuel, that is not a situation where the problem is causing NZ grief, but rather it has become one which threatens NZ's sovereignty due to the sheer amount of disruption a lack of fuel will cause.
EDIT: Additional comment. Some of the info on NZ's petroleum situation came from this
Stuff article, but other sources were found
here and
here.