Polyphemus,
You are digging yourself into a deeper hole. The recoil physics being discussed are precisely what change the vertical POI with bullet weight which is what the OP wants to find a way to compensate for. They also explain why he will have a difficult time trying to achieve matching POI by loading the lighter bullet hotter.
Here's what you seem to be missing: When pressure is made in the case, force is applied to the base of the bullet to propel it forward and, simultaneously, an equal and opposite force is applied to the breech end of the gun by that same pressure. That is the force creating the muzzle rise. Here is the mechanism:
In illustration 1., below, you see a force applied to an object with a pivot and it is not directed straight into the axis of the pivot. The result is torque which turns the object around the pivot. This is the same principle as pushing on a wrench handle to turn a stubborn bolt. If you then add a side extension that is aligned with the direction of the previous force, you get the same result (see figure 2.). It's no different than pushing on the wrench handle would be if your forearm suddenly got longer. If, as in figure 3., you reshape the pivoting object and extension like a gun, and you replace the force from your arm with the equal and opposite bullet propelling force and move the pivot to the center of support from the flesh of your hand, you can see you get torque that turns the gun on the vertical plane.
The force is applied all during the time the bullet is in the barrel, so the rotation has to be accelerating during that time, even though part of it is absorbed by starting the slide back, it also starts the barrel back if it is a locking design, tipping the muzzle up. Even in a straight blowback design, force is being applied against the frame through the recoil spring and through cocking effort. Unless you can make that zero, the muzzle will start to rise before the bullet gets out. And in a revolver or single-shot handgun, you don't even get that level of recoil absorption.
If the barrel were lined straight up with the pivot point, no torque would result and the muzzle would not rise. This is the idea behind barrel placement in a bullpup military rifle design. It is to eliminate muzzle rise in full-auto fire. Also, in the 1950s the Russians had Olympic rapid fire pistol designs that placed the barrel straight in line with the shooter's arm and had the sights extended way up above the barrel. The extensions made the barrel look like an inverted hacksaw frame, so these were referred to as hacksaw guns. I believe they were banned by the rules, as controlling muzzle flip was considered part of the competition. At any rate, they disappeared. But that gives you an idea how handgun design would have to change to avoid this issue of POI changing with bullet mass.
So, why is the change in bullet mass causing a POI shift? Even if the load pressure and amount of gas were identical for the two bullet weights, as they are in an airgun, the heavier bullet's greater inertia will cause it to take longer to exit the bore than a light bullet does. This gives that same force more time to accelerate the gun mass around the pivot before the bullet clears the muzzle, so the bullet exits when the barrel is more elevated, raising the angle of departure and, with it, the vertical POI.
Handgun shooters have long observed that bullet weight has more effect on point of impact than charge weight does. Increasing charge weight will raise the POI a little by pushing harder on the bullet and increasing the equal and opposite reaction force on the breech end. However, this also means the bullet gets out of the barrel faster so the greater force doesn't act for as long. It's not proportional because acceleration is a square function, but you do have to add a lot of charges to raise the POI of a lighter bullet to meet that of a heavier one, and it often isn't withing practical pressure limits of the cartridge.
An exception often occurs at longer range. A big, heavy bullet will have a high, arcing trajectory and since gravity accelerates heavy and light bullets at an equal rate, you can often find a distance where the heavy bullet has fallen to intersect the trajectory of a lighter, faster bullet. At that magic range, POI will match. Beyond it, the heavier bullet's POI will be lower. But for the short ranges most folks use a defensive handgun with, heavy bullets will impact higher and unless you are comparing a much reduced heavy bullet target load to a hot lighter bullet load, you won't likely make up the difference.
