I would approach this from a different angle...
If we agree that dogs are 1) predators, 2) pack animals, and 3) really want to get a bird in their mouth then you have to ask yourself since you are the Alpha in the pack "is the dog creeping in step for step with you really because the previous owner expected the dog to flush the bird?" or could it be that "the dog is creeping in because you are seen as competition to him in your attempt to get the bird that he found?" Moreover, you should also be asking yourself "if the dog is steady through the whole process and does not creep in after the bird, what is the reward for the dog?" Are you shooting these birds for the dog as a reward for doing the right thing?
Assuming there is some kind of reward for the dog performing to your expectations, if the dog is solid until you begin to walk in and then begins to creep with you, I would simply just step back away from the dog and bird and wait and see what happens. If the dog continues to creep, I would launch the bird and not reward the dog with a bird in its mouth. However, if the dog tightens up and is staunch, I would approach once again slowly and if the dog moves with me, I would back out again and wait. Only a totally steady dog that allows me to move in and shoot a bird for it gets rewarded with a bird in its mouth. That should teach the dog "hey, if I don't move and I let the Alpha do his thing, I get rewarded with a bird." On the hand, "if I try and move, either the bird is going to fly away or the Alpha is not going to move in and shoot me a bird."
All of the other suggestions will certainly work with many dogs, but timing and reading the dog is critical, otherwise the dog may begin to loose focus on the bird and begin wondering if he is going to get shocked, picked up, restrained, etc... while on point. This may take some dog's attention off the bird and while many dogs can withstand this kind of pressure, it could cause problems in other dogs.