From my reading of the Owners Corporation Act, two lot stratas are exempt from the legal requirement to insure common property which means it’s hard to compel your neighbour to do anything in regard to insurance.
I am pretty sure the people at CHU will have encountered something like this before so why not call them, tell them you want to gibve them your business and ask their advice. They are the expersta, after all.
By the way, your current insurers sound so lackadaisical I wonder if you are actually insured at all.