Bernie – If you win your dispute with your upstairs neighbour by using the VCAT process then VCAT will issue an Order for the upstairs neighbour to repair the balcony. Most people obey Orders.
However, if the upstairs neighbour still refuses to repair the balcony then you can take this matter further through the Supreme Court. Although it sounds burdensome for you to have to do this it will probably be the upstairs owner who will pay your costs.
See here for further details on what happens when an Lot owner does not comply with a VCAT Order:
I personally can’t see how you could obtain any other relief through body corporate insurance etc as this is outside of their jurisdiction.
If I was you I would try the VCAT approach as quickly as possible. The steps to take are outlined in the link above. You could use some ideas from the VCAT case that I linked to in my previous comment to assist in formulating your arguments.