Hi there

as a former New Zealand based Travel Agent is sounds to me like you have booked an LH fare - I realise the rules may be different as you are ticketed originating in Germany and I am refering to the rules ex NZ however in my experience this is ticketed as an LH fare not an NZ one even though there is NZ carriage - unless the rules have changed in the last few months LH's position is that the piece system only applies on a directional basis ie if you are going through the US in one direction you are entitled to the piece system only in that direction ( and only until your first stopover in Europe )

eg

NUE LH x/FRA LH x/SFO NZ AKL NZ x/LAX LH x/FRA LH NUE
piece system applies to whole itinerary

NUE LH x/FRA LH x/LAX NZ AKL NZ x/SIN LH x/FRA LH NUE
piece system applies from NUE to AKL but 20kg from AKL to NUE

NUE LH x/FRA LH x/HKG NZ AKL NZ x/SIN LH x/FRA LH NUE
20 kg for the whole itinerary

In New Zealand if the ticket has been inadvertently issued with an incorrect baggage allowance LH permit it to be reissued with the correct allowances showing - please bear in mind that I am describing the situation in NZ as it was a few months ago when I was still in the industry - it may have changed - and of course the rules may be completely different ex another country - such are the joys of the industry !

hope you have a great trip anyway