To understand why the same hanger number may not give the same point of impact result in every barrel type you first need to know how the hanger works.
K-80 barrels are separate along their length and the hanger determines the distance apart at the muzzle. Fitting a large hanger pushes the two barrels away from each other whilst a small hanger pulls them together at the muzzle. If both barrels moved equally the result would be a little difficult to shoot with because putting in a big hanger would push the bottom barrel down but the top barrel up whilst the smallest hanger would pull the top barrel down and lift the bottom up. That would be a bit confusing to say the least.
Of course, it does not work that way because the rib soldered on the top barrel acts like a brace and stiffens that barrel. This means that the majority of movement is bottom barrel only and this is more predictable. There is a tiny amount of movement in the top barrel but only at extremes when the force of pushing the bottom barrel down overcomes the stiffness of the rib. Different rib configurations will have more or less brace affect.
When we come to the Pro rib or the Trap Special it is another game altogether. Those ribs are not soldered all along the barrel and are only fixed at front and rear and so the stiffness imparted to the top barrel is different. It is still braced but in a different way.
Both the Pro rib and the Trap Special are adjustable and so the point of impact will differ depending on the exact setting of the rib adjustment because the rib changes both barrels. The adjustment also changes slightly the brace affect and is theoretically stiffer when lowered right down at the front.
Slight differences in barrel material will change the stiffness of the barrel and whilst Krieghoff barrels are remarkably consistent in dimensions and weight it will be the case that one barrel set is stiffer than another.
The centre hanger also has influence and it depends if it was clamped when the hanger was fitted or relaxed. If relaxed the barrel moves over it’s full length but if the centre hanger is clamped onto the serrations the barrel can only bend from the centre forward. Just slackening and re tightening can have a noticeable effect on point of impact.
As a rule of thumb, identical barrels in length and type, rib and configuration will use a hanger no more than one size either side of whatever is standard for that barrel type. If the standard is a #5 it will use either a #4 or #6. The factory pattern test every barrel and fit whichever hanger makes both shoot to the same point of impact.
As to where each hanger makes the pattern print is entirely down to the shooter. For one shooter a #5 hanger will shoot 50/50 but it does not follow that is so for another, even shooting the same gun. We all look along a gun differently and so it is impossible to predict. As a rule, when I pattern a gun it will shoot at least 10% higher for me than it does for most shooters. It is all to do with how you look at the target. Some use the beads as sights whilst others align them in their peripheral vision but look over the gun at the target.
Does any of this matter. I do not believe it does and I think shooters get too fixated on hanger number. Each hanger only moves the pattern a tiny amount, an inch or so. If you change from #1 to #8 it will not cause you to miss a perfectly centred target. You have at least 10″ or more above and below the centre so the target will still be in the pattern. The hanger is only to help put the centre of the pattern where you are looking and whilst. that is very worthwhile it will not make you hit targets you normally miss.
The human brain is an incredible computer and will correct the aim point after a very few shots. It does this by analysing visual feedback and identifies that the shots are a little high or low and corrects the aim point automatically and without any conscious thought.
If you are happy where your hanger shoots then never mind what anyone else tells you it does for them. Just shoot it and the targets will break.