The advice provided by the Department of Fair Trading is correct and the Sections of the NSW Strata Schemes Management Act (SCMA) that you’ve no doubt already found substantiate that position of only persons entitled to vote at a General Meeting being able to requisition Motions to be placed on its Agenda.
The only complication may be if the Agency Agreement (Contract) that your Owners Corporation holds with the Strata Manager has delegated them the role of Secretary, where that position is responsible for producing the Agenda for General Meetings, including Motions.
If it’s not too late, have the elected Secretary (of your Executive Committee) write to the Strata Manager to advise that they’re assuming the role of Secretary for the upcoming Extraordinary General Meeting (EGM), and instructing them to remove the Motion re their re-appointment from the Agenda.
Failing that, once the EGM commences, rather than implying acceptance of the Strata Manager’s Motion by again deferring it, you (as Chairman) have the ability to rule it out-of-order on the basis that it is in conflict with the provisions of the SCMA.
Before your Owners Corporation further contemplates termination of its Agency Agreement, have a careful read through all of its provisions – particularly those applying to it rolling-over if not renewed, and to the means of termination itself including the notice that the O/C must provide.