I am guessing you are in NSW. I am in the ACT where the legislation is a little different. Nonetheless, the Act would specify the form of notice required to call a general meeting. I expect that just a note on a notice board is not sufficient to call a general meeting. A valid notice of a meeting would, I expect, require a certain amount of notice to be given, for certain details about time and place to be on the notice, perhaps a particular form to be used, and all notices to be mailed to all owners at the address for correspondence that has been registered on a list of lots held by the OC.
There is nothing wrong with the EC proposing motions and advocating a yes vote for its proposals. Preparing proposals for the management of the OC is part of their job. Still supplying a proxy form with the boxes already ticked is a bit over the the top! I think in NSW the Act specifies how a proxy form appears in more detail than in the ACT. If the pre-filled form is the only one provided then I would expect you have a good case for saying it is not a valid proxy form.
I suggest you talk to your neighbours to gauge their reaction. Perhaps there is general dissatisfaction with the present manager? On the other hand, it seems like the EC has gone off half-cocked. If I were on the EC, and if I were dissatisfied with the present manager, I would be working with the rest of the EC to assess alternative managers, look at their terms, conditions and prices, checking whether other OCs were happy with those managers and only then present a case for a change along with a motion to engage a particular new manager. The EC does not need a general meeting decision to give it permission to research options.