I estimated an acre per tribe in Catalonia as a territory. A tribe could be a breeding pair plus offspring. There were no fences that would contain chickens so they have an entire National Park at their disposal. My usual range distance tallies with yours (I have to convert everything to metric)To have a robust flock of maybe 21 head of adult gamefowl with room to reproduce? 2-3 acres. Generally they stay within 200 yards of their primary roost 24/7 year round. For most of the year they stay within 100 yards of their roost. If you want to double the flock size to around 50 and ensure you have all the stragglers contained with a boundary they never cross, call it 5 acres.
If you’re talking about hatchery-bred chickens of commercial breeds, they’ll wander all the way across my 40 acres until they get caught by a predator. Except for the leghorns. They act very much like gamefowl in staying close to home and acting like they have sense.
Edited: the gamefowl never go 200 yards in one direction. It would be more accurate to say they stay within a 100 yard radius of their roost. I don’t think they ever go further than 150 yards in one direction. So actually they stay within a 200-300 yard diameter with their roost being center.
The layers will in fact go 250 yards in one direction.
More tribes meant pushing out into unclaimed territory. 4 tribes used about 4 acres. But, these were not gamefowl. They were French Marans brought in from France (free rangers) and Bantams with mostly English Game genes.
In the UK with over 500 free rangers mixed sex single breed, eight acres was about the limit. As each new generation hatched and grew there would be occasional groups that would push out further than the norm but as you noted, predation risks increased.
On my uncles farm four or five tribes lived on about 5 acres and didn't show any inclination to wander away from their territories.
I should point out that in all the above some commercial feed was supplied.