KT the problem you have is common. The thing that happens here is the difference in the angles and speed. Not the distance. The average person uses the swing through method of shooting. The big problem in this though is the fact that you aren't looking where you should be. This is the most common problem in all shotgun shooting. You should only (always) be looking at the target(bird). When you try to swing through the bird you have a tendency to look at the front sight of the gun(only way to tell if you are in front of the bird ya know?). The best thing to do when shooting the big rivers etc is to pay attention to the part of the bird you want to hit and forget the lead thing. If the gun is on your shoulder where it should be the little ballistic computer between your ears will tell you when to shoot. TRUST that little thing 'tween your ears. You can't hit many looking at the gun. Oh and when you are looking at the part of the bird you want to hit....always pick the beak. Think of this...shooting geese...a gooses head is about the size of a dove. Ever shoot doves?? Geese and ducks fly just as fast as doves y'all. seriously! Ya don't hit doves looking at their breast...geese or ducks either! BTW you also have to make sure that the gun fits fairly well. Winter and more clothes makes summer's gun too long.
Lots of other things I could tell ya but not enough time now