No worries.
Our green list roles are a bit limited honestly, my partner does data engineering which isn't covered in the list. She ended up studying and applying for a Post Study Work Visa. It requires you to complete a degree in NZ and then you can have up to three years to work and aim for residency. We have one year master degrees, this is what my partner has done. Perhaps you could even complete your PhD here, I don't know what that process would look like though.
But.. our international student fees are expensive.
I didn't ask for this bs