I do the "impossible" with free-range chickens having minimal losses so I'm an advocate of letting them run. I also have a handle on the value of forages and the ability to exclude predators from an area large enough to support a flock of chickens. If the "safe zone" is not a least a large part...
I have similar issues although the quality and quantity of forage here is likely a lot better than you have. The better the forage, the less acreage needed. At some point the fencing becomes too expensive.
I'm of the sort that is outside a lot and uses a range of approaches to keep predators at bay. This includes a combination of cover, poultry guarding dogs, and fencing. My flock is closed with all replacements bred on farm even though all are free-range for at least part of their lives.