YNZ is irrelevant, although could be used to show history along with other receipts such as marina fees, insurance etc for evidence of historic ownership at time of registration if for any reason you needed to prove "ownership" if it was ever challenged...
Your registration papers are official they have your name against them as the owner if it's not you then it's the company or trust.
The Tax paid status of the vessel is independent of the registration and is tied to the owner.
When you leave NZ the vessel is fundamentally exported as goods. This doesn't mean you get a gst r