New Zealand Law
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Under the Residential Tenancies Act you can apply to the Tenancy Tribunal to cancel a fixed term tenancy if certain grounds are present. The Act says at section 66,
Reduction or termination of fixed-term tenancy
(1)On application by a party to a fixed-term tenancy, the Tribunal may make an order reducing the term of the tenancy by a period stated in the order, and making such variations in the terms of the tenancy as are necessary because of the reduction of the term, where it is satisfied that, because of an unforeseen change in the applicant's circumstances, the severe hardship which the applicant would suffer if the term of the tenancy were not reduced would be greater than the hardship which the other party to the tenancy would suffer if the term were reduced.
(2)Where the Tribunal makes an order under subsection (1), the Tribunal may order that the applicant pay to the other party an amount determined by the Tribunal by way of reasonable compensation for any loss or damage to the other party
The heat pump issue alone would not justify this, as the tribunal would say you should have applied at the time to get this installed rather than wait until now.
The verbal notice to quit was not enforceable anyway, as she must wait until the end of the term, and any notices must be in writing. But you are on the right track with the offers to find a new tenant. You can certainly negotiate that if the the landlord agrees.