If I was you, I would stick with BA at least initially. X1 return to SIN booked with BA (ie BA15/16 and a codeshare transtasman) gets your 4 BA flights, then you’ve got scope to use QF, CX etc

keep an airpoints account on the side for the domestic legs where NZ is the only option, and if you end up traveling SQ, flybuys etc. Although airpoints seems to be “even worse” than QFF