I hate putting up fence, what a job. The run we have up is very small compared to what you have, it's only 140 sf, but they get out three days a week to free range, and next year when I have more birds I'll probably start looking at the maypole idea over the yard, and bird or hail netting over the new runs. The chain link roof over the chain link run is one of the most comforting things we've ever done, but it was expensive and really challenging physically. One morning this week as I walked out to open the pop door and leave the day's meal, I heard an owl very nearby, and was glad the roof was sturdy. I leave here around 5:15, so this time of year LONG before sunup. The girls make little noises to let me know I've awakened them, but it's dark and they don't budge from the coop.
For youngsters, especially those of an age to not be sure how to get back to the coop, I wonder if just a small shelter in the run might help? Like an overturned wooden box with a chick sized doorway cut into it - heck, even a sturdy cardboard box with a weight on it would work as a temporary solution - but of course those things only work if the chicks are savvy enough to use them

I confess I didn't let my Sussex out until they were probably 4 months old, for about the same reasons, but the first day I did, the pigeons from the barn flew overhead and they all ducked and looked up and prepared to run for cover if they needed to - exactly what I wanted to see from them. I waited until I knew I would be here the entire day to try it, in case we ran into problems.