I would not advise you to do anything except press your case through mediation and, if need be, an approach to NCAT.
In the meantime I would advise the strata committee that, by refusing to consider the application, they are in breach of their duties under Section 232(2) of the Act, regarding failure to fulfil their responsibilities.
In the meantime pay your $34 to get a copy of the strata roll (consider it a penalty for jumping the gun on rubbish collection) and then write to all owners explaining that you want to do the right thing and you want to avoid any unforseen consequences but the committee won’t let you.
How that will be regarded on the committee is impossible to tell but you might want to slip quietly into the conversation that you could be looking for compensation if this costs you financially.
If you want the nuclear option, apply the NCAT (directly) for the appointment of a compulsory strata manager. That would get their attention.