We were planning to include NZ and OZ in a OWE and note that the choice of carriers really thins out in that region, and some of the Pacific island nations that might be attractive (Tahiti, Maldives, Seychelles, etc) don't seem to be accessible by OW carrier.

Any eligible code-shares, fifth-freedoms or second-label carriers or anything else I'm missing?

Interestingly, QF seems to have rights on at least one domestic NZ route, Queenstown-AKL, although they fly it infrequently.