You have to know what motivates your particular dog in order to know how to redirect its behavior. I don't believe there's any training method that will work 100% of the time with 100% of dogs. OP has a great deal of training experience so I would hesitate to second-guess her, but it seems to me that her dog has now experienced the most exhilarating process possible for any dog - the adrenaline high of a chase followed by a delicious snack. It's hard to think of any training method that would convince any dog to not go for a repeat. I would think that separation is the safest method . . . even after tons of training, if one slip-up results in the death of one or more birds (and the loss of time and money invested in those birds) what's been gained?
We have greyhounds, who are bred and trained for hunting, so I'm not willing to let our dogs mix with our birds at all. But each of the two dogs have different personalities, and while one has so far shown no interest in the birds in the run, the other gets no greater pleasure than to run at the fence and make the girls scatter . You can see the joy on his face as he does it, and no amount of scolding on my part has changed his mind, in spite of the fact that he's the easiest one to tell NO in any other situation. In his case, the reward of seeing the girls run and squawk is far greater than ANYTHING I could offer as a substitute. Which is why the dogs get locked in the house when I let the hens into the yard.
In any situation where a dog is doing something that you don't want, you have to figure out how to convince them that NOT doing it is better than doing it. Hard to do when the bad behavior results in a chicken snack.
But it's really not that hard to keep the birds and dogs separated, and then you can enjoy them both.
