Fitting makes the gun fit you and point at what you focus, or concentrate on. So how is lead established? If you move the muzzles ahead of the target then the gun is no longer pointing what you are looking at, or you are not looking at it bt at the sky ahead of the target.

Could it be that the situation is not so much hard focus on the target but more an awareness of relationships between muzzles and target? Neither one being in super hard focus?

The quiet eyes methods seem to be pointing that way, though they were not evolved with shotguns in mind.

Funny though that hitting a moving target with a rifle type sighting setup involves focusing on the front sight, as in stationary shooting, yet manages to work just fine.