SAS have said "No" so it's back to planning. If I change the SYD-CHC-AKL to SYD-AKL then the saved mileage allows either EDI-LHR-BKK or EDI-FRA-BKK.
The CHC-AKL leg was due to be surface as we are hiring a Camper Van to tour the North and South Islands. We will probably redeem miles for a CHC-AKL flight.