NCAT has the power to order an Owners Corp to allow work to be done. Have a look at section 140 of the Act (below). Note that it specifically mentions the previous behaviour of both parties, including taking into consideration whether or not the lot owner applied for permission.
Your best bet may be to canvass other owners before they have a meeting and let them know that, while you would rather settle this amicably and with all necessary protections for the Owners Corp in place, you plan to pursue this all the way to NCAT if need be.
Significantly, if they follow the chairman blindly, they could be up for tens of thousands of dollars in legal fees and still have to give you permission. You might also want to write to all owners and not just the EC, warning them of the unnecessary costs they might be facing.
At the same time, be as reasonable and accommodating and ‘legal’ as possible so that any objective assessment would reveal who was at fault here.
By the way, as a member of the EC, you can very simply propose a motion that the chairman be removed from office (though not from the EC) and replaced by someone else. If this guy is as autocratic as you suggest, then you won’t be the only person who is tired of his antics and all it requires is a simple vote by EC members to remove him from that role (provided you have someone else on the EC prepared to replace him).
140 Order relating to alterations and repairs to common property and other property
(1) An Adjudicator may order an owners corporation to consent to work proposed to be carried out by an owner if the Adjudicator considers that the owners corporation has unreasonably refused its consent and the work relates to any of the following:
(a) alterations to common property directly affecting the owner’s lot,
(b) carrying out repairs to common property or any other property of the owners corporation directly affecting the owner’s lot.
(2) An Adjudicator may make an order approving of alterations or repairs already made by an owner to common property or any other property of an owners corporation directly affecting the owner’s lot if the Adjudicator considers that the owners corporation unreasonably refused its consent to the alteration or repairs.
(3) An order under subsection (2) is taken to be the consent of the owners corporation to the alterations or repairs concerned and may be expressed as having effect from a day specified in the order that occurred before the order was made.
(4) An Adjudicator may specify in an order under this section whether the owners corporation or the owner of the lot concerned has the ongoing responsibility for the repair and maintenance of any additional property arising out of an alteration or repair to common property approved under the order.
(5) If an order makes provision for the owner of a lot to have the ongoing responsibility for the repair and maintenance of any such additional property, the order also has effect in relation to any subsequent owner of the lot.
(6) In deciding whether to grant an order under subsection (2) or to provide for the order to have effect from a day that occurred before the date of the order, an Adjudicator may take into account the conduct of the parties in the proceedings, for example, if an owner did not first seek the consent of the owners corporation before carrying out the alterations or repairs.
(7) An application for an order under this section may be made only by a lessor of a leasehold strata scheme or an owner.