According to this factsheet the balcony slab is common property but, unlike in NSW, anything attached to it is lot property, and that would include the membrane. However, the owners corp can agree by special resolution to fix lot property, especially if it affects other people. That said, it sounds like they are unlikely to go down this road.
Also, I wonder how we can be sure the problem is entirely in your lot and not the adjoining one with the shared balcony. The 10-year building warranty claim may be your best bet but I would be trying to get the people below and the people next door to pressure the strata committee to engage in supporting your claim, rather than just washing their hands of the problem.
They’ll be glad of your assistance when the next balcony and the next one after that, starts to leak.