If you have satisfied all the requirements of the renovation, including proposing a by-law that transfers responsibility for any affected common property to you, then the Owners Corp has no grounds for refusing.
In that case, you would seek relief through Section 126 (2) of the Act (see below). I would think that explaining this to the other owners, and pointing out that you would also seek to have costs awarded against the OC if you were forced to go down this road, would focus their minds.
Strata Law doesn’t require equality – just fair treatment. Denying you the option to do something because they can’t is not fair provided your plans don’t impact negatively on other owners.
126 Orders relating to alterations and repairs to common property and other property
(2) Order consenting to owner’s work on owners corporation property
The Tribunal may, on application by a lessor of a leasehold strata scheme or an owner of a lot in a strata scheme, make an order (a work approval order) approving of minor renovations or alterations or repairs already made by an owner to common property or any other property of the owners corporation directly affecting the owner’s lot if the Tribunal considers that the owners corporation unreasonably refused its consent to the minor renovations or alterations or repairs.