Well, Supersleuth, as they say in all the best crime novels, the answer is to follow the money.
I’m not saying your EC secretary is corrupt (even if you are) but if he isn’t doing the right thing it will almost certainly be costing you money.
The simplest way is to find a local real estate agent who says if you had done A, B and C rather than X, Y and Z, your properties would be worth more. Then you get that message out to the other owners.
The simplest way is to look at your sinking fund and sinking fund plan. If either is inadequate, it will diminish the future sales value of homes (as well as taking you down the slippery slope to special levies).
If you want to play hardball, start issuing a monthly newsletter about problems and, most importantly, solutions. Anybody can ask questions but the people with answers are the ones who get elected.
By the way, be very careful not to make it personal and especially not to make accusations that wouldn’t stand up in a court of law. However, if you present a picture of a dysfunctional EC that is costing owners money, they will soon draw the right conclusion about who specifically is to blame.
Your legal avenue would be to seek the statutory appointment of a strata manager but unless there is open warfare, clear signs of corruption and the building is suffering as a result, NCAT probably won’t have a bar of it.