Inconsistent baggage allowance on NZ Award ticket with multiple flight segments

Have an award ticket in July with multiple segments on NZ but baggage allowance throughout the journey is not the same:

Outbound: LAX-AKL-NAN (2 free checked bags allowed)
Stopover: NAN-AKL-CHC (1 free checked bags allowed)
Inbound: CHC-AKL-LAX (1 free checked bags allowed on ZQN-AKL segment. 2 free checked bags allowed on AKL-LAX segment)

I will take the lastest flight from CHC to AKL and the flight AKL-LAX will be the next day. Time interval between ZQN-AKL and AKL-LAX is less than 24 hours.

I called NZ and the agent told me that my 2nd checked bag on the NAN-AKL-CHC and CHC-AKL segments will be charged. I explained to the agent that my trip will start from the US so I should have 2 free checked bags all the way throughout the journey, but the agent told me "No" and it's the problem on the UA side and asked me to call UA to address the issue. NZ can't do anything about it but have to charge me for the 2nd bag. I understand that Star Gold member can have 1 extra free checked bag, so it should be ok for me to check 2 bags with any extra fee but I intend to check total 3 bags that contain my scuba-diving and skiing equipments, so 2 basic free checked bags throughout the journey is important to me in order for me to check in 3 total with any charges.

Any advice? What can I do?