Bung: In Max Cryer's "The Godzone Dictionary: Of Favourite New Zealand Words and Phrases" he states that the settlers adopted the word from Maori first print appearance 1820. At that point there were over 100,000 Maori and only 200 - 300 settlers.
When I learnt the meaning of pakaru 40/50 years ago I remember being told it came from ‘buggered-up’ and because I thought that was interesting, it stuck in my mind.
However that doesn’t mean it’s gospel and there’s certainly no reference to that on the ‘net. OTOH there are plenty of references to pakaru > puckeroo so it’s clear you’re right on that. And Max Cryer was definitely a respected authority on these things.