I think you are clutching at the wrong straws here. This rental agent is not a property manager by any accepted definition in relation to proxy votes and wouldn’t be even if his office was in your lobby.
Firstly, do you have a by-law banning short term lets? If so, that makes the following a lot easier.
If you have an existing problem with short-term lets, then you need to pursue that through your strata manager, Fair Trading, the Tribunal and your local council.
Meanwhile you should canvass the owner-occupiers of the block to approach the council as a group to make it clear that the law-abiding members of the community who actually live there do not agree to to approach by absentee investors who have hijacked the owners corporation.
You could even make a submission to NCAT (the Tribunal) to have a strata manager appointed to take over from the EC. Or you could ask for orders for the creation or enforcement of by-laws restricting lets.
Finally, if this rental agent is already managing illegal short-term lets, then you should complain to Fair Trading. By the way, a recent ruling by the Land and Environment Court said that short-term lets are not covered by the Residential Tenancies Act. So if this agent is promoting short term lets in a residential-only building he is breaking the law.
Illegal short-term lets are a cancer in strata. Hit them with everything you’ve got. Best of luck