If the matter is to be decided at an AGM, don’t rely on the EC to do all the work for you. You are a member of the OC so you can propose a motion and word it how you like and provide whatever background information you like. Keep it brief so the OC does not have to provide many pages in the meeting papers.
It sounds like you can put a motion to the general meeting: ‘That installation of an air-condition be approved on the xxx wall for unit X noting that it would not be visible from the street in line with the bylaw X, that this is the most practical location for unit X, and that it would not provide a precedent for other units to install air-conditioners in locations other than on their balconies because unit X has a unique configuration – a smaller balcony and access to the xxx wall.’
Is it possible the EC members are not actually opposed to the proposal? Perhaps they are just being cautious to avoid making a decision that they worry might be contrary to the spirit of previous decisions on air conditioners? If so, they might be happy to support your motion at the general meeting. Regardless of that, if you can convince other owners that your proposal is fair and reasonable then you can carry proxies of your own or encourage them to attend the meeting.