I think the question to be asked is, what is your motivation for wanting to let your flock free-fly outside of their aviary? Going by your original post, it doesn't sound like this was something you really wanted to do that much before the birds escaped.
I've met a lot of people in pet stores who believe it's morally wrong to keep birds in cages and express the desire to set the birds free (even though we live in Canada, which isn't the friendliest climate for tropical birds, and companion birds bred in captivity have no survival skills to begin with). For most of us who take care of and love our birds so deeply, cages, bird rooms, and aviaries aren't treated as prisons for our birds - they're treated like our birds' bedrooms or houses: a safe retreat where they can play, and eat, and sleep as they please - and spend most of their time out with us. Akimi spends almost all of her time outside of her cage when I'm home, and even though she can fly, she chooses not to most of the time 'cause she's a lazy bum.

The point I think I'm trying to make is, is that for all the freedom you can potentially give your birds by letting them free fly outside on their own, you also have to face the fact that letting them have that kind of freedom will likely cost your birds their lives. They are not wild birds. They don't know how to avoid predators or cars or cruel people. They don't know how to tell which plants are poisonous and shouldn't be eaten or chewed. They can easily contract diseases from wild birds and other animals. Even if they know to return to their aviary for water and food, if they wander too far and can't find their way back they might well die of starvation or dehydration - which are terrible ways to die and cause a lot of unnecessary suffering for an animal that would otherwise be well cared for.
You also have to consider that if they defy the odds and thrive flying outside, you could well end up unintentionally introducing an invasive species that could do incalculable damage to local ecosystems, and force native wildlife out of their niches.
For most of us who are very close to our birds and concerned for their well being, the thought of our beloved companions suffering any of these terrible fates because we wanted to let them fly free in our yard is devastating. This is the reason why you've found so many people on here who are against the idea. It might offer our birds more freedom to let them free-fly outside, but for us the cost of giving them that freedom is much higher than any of us are willing to pay.