If you have the numbers (ie, 75 % of those voting in person or by proxy), at your EGM propose that all seats on the EC be declared vacant. Then a new election is declared at which point you can first, choose the number of seats on the EC, then elect people to those seats.
If you don’t have the numbers to vacate all the seats on the EC, you will have to persuade the sitting members to resign. It doesn’t sound like that’s going to happen. If that’s the case, you will have to wait until your next AGM (where a imple majority will decide the size of the EC and who is elected to it.
If you do go ahead with the EGM, the best way to get the proxy votes that you will almost certainly need and which are probably being held by the chair is to tell owners (directly, by mail or phone if need be) how much the value of their property is suffering under the current EC.
If at all possible, don’t get into personalities – nothing turns people off quicker than what seems like spiteful sniping. Get local Real Estate agents to tell you how much better property prices and rents would be if the building was being managed properly. The more specific improvements you can mention, the more likely you are to convince people.
The day before the AGM, make sure your supporters are all fully paid up on their levies (or their votes won’t count) and be prepared to challenge the incumbents on that and the validity of their proxy votes if need be.
Best of luck … and be careful what you wish for.