It seems that booking classes have changed for this fare as follows:
NZ - T (international), M (trans-tasman), H (domestic), Z (business)
SQ - M, Z (business)
VS - X, Z (business)
Unfortunately, T-class earns 0% on UA. A travel agent informed me of the above. I then called NZ to confirm who says their flights are in Q (not T). So then I called another agent who confirmed T, then VS who confirmed T, then NZ again who confirmed T.

