Can you make some investments into the property? You can kill and trap foxes all day long, but if you don't have a controlled population they'll just be back, won't they? It sounds like the chickens need a safe run, the dogs could use a fence (that doesn't sound like much of a life for an active breed) or they need training.
To me, free-range = loss. It makes me sad to see predators wounded and suffering (if you're not sure of a shot, I wouldn't take it) because we essentially set bait for them in our yards. If you range chickens without employing a dog, etc, they're not safe. It's just the nature of the beast.
To me, the ideal situation would be to make an investment in the dogs, Train them to be poultry-safe and not run off. Use training collars if need be. Because them being kenneled is a waste in your situation and probably really depressing to them. I hope they have their own run, at least.