If I were to try and solve it, I would try several things.
1. White bumpers on short grass to teach "bird by gun" (she tumbles ass over head on these trying to stop).
2. Salting the area with birds and stomping down a lot of grass in the area as well as running her last to teach her to recognize the small of birds and or foot scent/disturbance
3. Gunner help (although I would rather she self discover where the bird is).
4. I think the 'dirt clog drill" is designed to help with this but have never used it.
5. I might use terrain on a limited basis to create a wall behind the fall, in order to prevent her from running long.
6. Just let the dog mature over time and get more experience.
It's all very passive teaching so it would take a while to cement.
I have always been taught that pressure in that proximity to the gun is a terrible idea and I can see why, so I wouldn't choose that method.