If this were the ACT, I would look to the default rules (aka bylaws) that:
-require a unit owner to repair and maintain their unit, and
-require a unit owner to not use their unit in a way that unreasonably interferes with the reasonable use and enjoyment of anther unit, and
-allows a representative of the owners corporation to enter a unit if reasonably necessary for repair and maintenance subject to reasonable notice etc., and
-the provision of the Act that allows an owners corporation to resolve at a general meeting to take on certain maintenance tasks on behalf of units owners that would normally be a unit owner responsibility.
Between these provisions, I think you could mount a case for and provide the process by which the OC could require the maintenance to be done on all balconies for the benefit of other units and the building as a whole and for the OC to undertake that maintenance and to have access to all units for that purpose, subject to reasonable notice etc.
I assume that other jurisdictions have similar provisions. You would just need to string them together and have the relevant vote and then nobody could refuse and all would be up for sharing the cost. Whether the cost was from the sinking fund (with an amendment to the sinking fund plan) or billed at a flat rate or by unit entitlement to each unit would be another part of the resolution.