It really doesn’t matter who puts forward any new Strata Manager at the EGM as long as there is a motion on the agenda to appoint that managing agent. There is no restrictions on who within the OC can put forward a Strata Manager, any owner entitled to vote can submit a motion on the agenda of an EGM, that includes to appoint a new managing agent.
I don’t think you need a special ‘committee’ to obtain quotes from various strata managers, the EC can certainly do that. Just remember it will be up to all of the owners at the EGM as to which Managing Agent is chosen. In my view forming an ‘independent committee’ may be pointless, as the EC or any owner can recommend a Strata Manager.