Thanks very much. I am hoping that someone has also done some research into it and maybe came to different conclusions. I have the Dogfights DVD's and this engagement is described on Season One, disc one. You can also see Colonel Anderson's description of the fight here on Youtube (forward to 45m:18s:
https://www.youtube.com/watch?v=a9sQg3XkGLg The fact that Anderson repeats the recollection of this action so often in his interviews is testimony to how greatly it impressed him.
Here is the actual 27 May 1944 gun camera footage of the fight on Youtube:
https://www.youtube.com/watch?v=-WVxB5MBdYE Obviously the camera only operates when the guns are fired so it is very short, whereas the battle itself was quite extended in duration and the advantage changed hands several times.
Cheers!