The problem is many shipping agents you choose in the overseas company have agreements with local NZ shipping agents. So it's not like you choose ABC Shipping from the UK and assume you will have to sort out brokerage/clearance details at the NZ end - they most likely have someone appointed that can easily name the terms of the costs.
Believe me, the costs of the handling fees is the last of your concern. It's dealing with MAF that can be a mega problem because quite often, you have no way of knowing how well cared for the container has been during packing and in transit.
MAF does inspection at a sealed quarantine zone. If they find that the container had sweated a lot (ie. a tropical cruise around east asia) and finds your vehicle has mold growth on the upholstery, expect more costs. You will have to pay for the cleaning of the vehicle, methyl bromide treatment, + a 2nd MAF inspection.
I think you may be too late at choosing a different NZ broker if they've already invoiced you. Normally, you could appoint a different broker PRIOR to the container arriving.