1. On the face of it, there doesn’t seem to be any reason why the EC would object to your application. The other two enclosures having been enclosed with approval would likely be relevant, if approval for yours were refused and you had to take it further.
2. The EC/OC probably should have required by-laws for the other two balconies, but that isn’t necessarily relevant to you. It is prudent to require a by-law in these type of circumstances, and in those circumstances the person carrying out the works is usually required to pay for the by-law. The works aren’t benefitting the other owners, so therefore you should pay for the exclusive use by-law which presumably will provide that you are responsible for ongoing maintenance etc. Enclosing the balcony benefits you, it doesn’t benefit anyone else.
3. How long is a piece of string? I would use the frequency of the EC meetings as a guide. Provided you give them all the necessary information/specifications etc., if there is no progress after a couple of months then I would start asking why.
More generally, you might want to suggest that an exclusive use by-law be drawn up covering all three of the enclosed balconies, i.e. yours and the other two previously approved. You say the EC has changed, so obviously their approach has changed, and they are doing the right thing. It could be worth pointing out that this gives them the opportunity to be consistent across the board, because otherwise the OC will be responsible for any maintenance of those other two balconies. If they agree, then the cost of the by-laws could be shared between the three owners.