Easter Eggers, not Ameraucana, are outstanding free range birds. They are ridiculously agile for such heft birds. My flock is about 50% Easter Egger at the moment. A healthy crow population on the property will help to significantly reduce aerial predation and also serve as an early warning for ground predators. Without crows regularly patrolling the area, I wouldn't ever consider free ranging.
You will need to deal with the fox before you can free range. It's likely the same fox that gets repeatedly treed by the dog. The second you let your birds out, that fox will start taking them. Bears are everywhere around here, and are very habituated to people, but they show little interest in trying to catch a chicken. They prefer easier meals, like chicken feed.
