When I was younger and could hear like no other, it "seemed" I killed more right after fly down, just in the first hour or so. I also killed more throughout the day, some late afternoon, as I did not have a family or other competing interests for my time. I suspect I was more aggressive and more careless as well, which resulted in me bumping them or killing them right off the bat. I had more birds to hunt back then as well, so if I bumped one, I could usually hear another gobbling off in the distance to go after. Now that I am older, and cannot hear as good in my left ear (closest to the gun barrel), with fewer birds to pursue, I'm more cautious and conservative than years ago. I definitely kill as many, or more mid to late morning, as I do in the first hour. Many times after they have left their hens, separated from the flock, or just settled down enough to call them to the gun. 99% woods setting for my hunting.
Andy you bring up a good point in that you specified your typical hunting setting. That's probably pretty important for bird behavior. I too am almost always in the woods setting.