Mediation is just the initial obligatory step before adjudication and perhaps a hearing.
At adjudication, each side presents their argument in writing. Whoever loses usually then asks for a tribunal hearing where you can present your case in person.
What you would be seeking is a CTTT order for your EC to obey the instruction of the Owners Corporation. In an extreme situation – such as the EC being seriously dysfunctional or just not running the strata scheme for the benefit of the majority of owners – you would ask for the compulsory appointment of a strata manager (although you have to find one in advance who is prepared to take on the role).
Proxy farming is a blight on strata in this state which is why it will soon be outlawed. But there’s nothing to stop you approaching owners directly and getting their proxies to hold a general meeting – proxies are extinguished automatically by a subsequent proxy – reverse the EC’s decision and, if you have the support, boot them out.