Finally got to the bottom of the insurance problem. Apparently unless you already have home/contents insurance in NZ, you can't get a policy for storage. Also, insurance companies that insure your goods in a storage unit on behalf of the storage company, wont insure you privately. In other words, each storage unit has its own insurance provider and that's that!
Crazy way of running an industry if you ask me.
Anyway, the long and short of it is that I told my storage company I would go elsewhere for the final time yesterday - big surprise - they rang me last night to say they'd got the insurance down to a third of the original quote!