mac, you really don't have to jump through hoops like that to find out how your gun and loads perform. And don't get hung up on 40 yards. That distance is a convention, as in my gun shoots 10" high @ 40 yards, or a full choke gives 70% PE @ 40 yards. Other yardages work as well.
You've already discovered that you can easily adjust POI at 13 yards. Multiply by 3 and you have offset at 40 yards. If you hit the cross hairs at 13yds you have a flat shooting gun. At 40yds, the pattern center will be at your aiming point. For every 1" of height above the cross hairs at 13yds your pattern is raised 10% above your POI.
Say your gun is set up so that it shoots 2" high at 13yds. That means it shoots 6" high at 40yds. Converting that to percentages, it is a 70/30 shooter.
Patterning at 40 yards is a convention. It is a good way to compare different combinations, but it is very hard to convert percentage info from 40 yards to another yardage. Patterns don't develop linearly, so your choice of choke plays a factor. Fortunately there is an easier way.
You are interested in real world results. How does my rig work for the targets I shoot at the distance I shoot them? Easy. Estimate the average distance you take your singles targets (or have a friend watch you shoot), then pattern at that distance. The choke shell combination that puts 85% of the shot in a 30" circle at target distance give you the best chance of breaking the bird.
Say you take your singles at 34 yards. You pattern various chokes and loads at 34 yards, count pellet holes (or use Shotgun Insight). Say you have a pet load and you tried 3 chokes and they returned 80%, 85% and 90% PEs. If you use the 80% choke you will have to take your birds about 2 yards sooner to get the optimum pattern. If you shoot that choke at 34yds you will lose an occasional well-centered bird. If you use the 90% choke you would have to slow down and take your targets later, otherwise your pattern will be tighter than it needs to be.
The 85% PE at target distance works. Give it a try.
Good word pic ZZT. One way of (looking) at a 40 yard pattern that's beneficial for longer distance shooting. If you can't see much of a pattern center (approx) with pellets spread wide, you don't have enough choke for the job.(added) For shooting from the 27 and farther back, games. Hap