I think you meant YVR-JFK not YYZ, as there are no OW YVR-YYZ flights and the CX transcon is YVR-JFK.
On the AKL-HKG-NRT-LHR segments, are you stopping <24 hours in NRT too(I note you are in HKG)? If you are, i.e. if you are attempting to comply with the transit Asia on the way to Europe from SWP rule, this will answer some questions on whether this multiple city route could actually be ticketed. What airline is issuing this routing on a OWE ticket?