I have a few days when I won't be home at dark, and don't let mine out those days. They aren't happy about it, but like yours, they have a large run. When both my DH and I worked full time, they only got out when one of us had a day off. With staggered schedules, they got out 3 days some weeks, 4 days on others. Now they only have a day once in a while that they don't get out.
There's a thing you can make called a "scoot 'n hide", when you have aerial predators. It's just a sheet of roofing tin, or plywood, or what ever you have handy, set up on cinder blocks or whatever you have, with weights on the corners so it won't blow away in a stiff breeze. If you place a few around near where the chickens tend to hang out, it gives them a place to scoot under when a hawk appears-and they will use them, they have good instincts. In Florida you might have to move then frequently, so you don't get snakes living under them, though.
BTW, white chickens are more easily seen by predators. Bright gold (like BO's) is also fairly easy for them to spot. My darker chickens, and brown-patterned birds hardly ever get nailed by anything.
