Can't help with the availability question.... sorry
BUT.. the
type of "Business" class you get depends on the a/c. AFAIK the LAX-NAN-AKL flights (and some AKL-SYD) are operated by the 767.. with "old fashioned" C class... 50" pitch recliners...
The AKL-LAX non-stop will be a 744 (normally) .. with the new Business Premier flat beds...
CNS-AKL only flys 4 days a week (Tue/Wed/Fri/Sun) and is also a 767...
Hope that helps!
P.S. The other AKL-SYD flights are A320's... C class is a 42" pitch...