While there are a lot of good points in your analyses, there are a couple of misconceptions:
Let me describe the shot cycle in energy terms:
The spring is compressed by your hand: the lever ratio is about 7 to 1. Compression force is about 40 lbs. That makes the total force compressed in the spring about 280 lbs FORCE, or 127 Kgs. or 1250 Newtons (Approx.) this is kX.
X is about 0.2 m, just for the stats, we will not use that datum.
When the piston goes forward, the temperature inside the piston raises to about 3,000 °F for a very short time, about 1 milisecond. This burns a little of the chamber oil and yes, there is MORE energy there than the one we put into the spring. It's not that it appears from nothing, it was there as chemical energy, we just transformed it into mechanical energy. That is why people hone the inside of the cylinders, to make them "hold" more fuel. If you truly want to use an airgun as a pure airgun, you will hardly get 700 fps from a gun that usually develops 900 fps. Yes, we use chemical energy in our airguns. That is why we tune them and lube them and maintain them. Most of the energy is given to the piston in the first 1/4 of it' crazy race towards the transfer port. The piston gets totally decelerated in the last 2-3 milimiters. The decelerations applied are of about 2-5,000 g's depending on the model and brand.
But the energy that got transferred to the pellet is not the spring energy, it is the combined piston's kinetic energy plus the little chemical energy of the controlled combustion. That energy gets put into the air that was scooped when the cylinder moved forward and the piston remained behind locked by the trigger. The air is just the MEDIUM through which one energy goes from one place to another, from the piston to the pellet through the transfer port.
Now, the air, at that temperature is not a gas, it's a plasma. And plasma physics are somewhat different from normal gaseous physics. Plasmas can go through small holes almost without friction. (CO2 is not a plasma, on the contrary, CO2 is "sticky", viscous. You can expect all sorts of strange things from CO2). So that is why Transfer ports have very little difference and why manufacturers can get away with using the same TP's for both calibers. They shouldn't, but they are.
But whatever the manufacturers do, they cannot ride above the laws of physics.
If the piston's energy "runs out of steam", then the total energy output will be lower than the base case. If the expansion ratio is so low that the pellet cannot absorb all the available piston's energy, then the pellet energy also goes down.
Let us take a D-48 in .22" as a base case. This is a 23-24 ft-lbs model. If you look at most published figures, those energies are obtained with pellets in the 14-15 grain category. If you take the same powerplant and connect it to an 0.177" barrel, then energies go down to 20 ft-lbs tops. If you take the same powerplant and connect it to a .25" cal. barrel, then energies ALSO go down to 18 ft-lbs in the best of cases...
The barrel length is one of the aspects that define the expansion ratio. For large guns like the 48 with quite a lot of swept volume, some barrels should be longer, but they cannot depart from the relatively standard shape and design of the gun. So, again, performances vary between calibers.
Coming back to the main and initial question: Heavy for caliber pellets fatigue the spring before medium weight pellets. Yes there is no doubt about it. I posted some time back a slow-motion film of a Kalashnikov recoil spring; and how it bounces back and forth before settling in again. This is because the Kalashnikov does not use a tight fitting guide like the ones our tuned guns use. The spring goes back and forth several times and this equates to several operations per shot. So, yes, springs fatigue earlier with heavy for caliber pellets.
If you have a good guide, then you minimize the effect.
If you have a larger caliber gun you minimize the effect.
If you keep your gun in tip-top shape you also minimize the effect, but it is there.
Now, having said that, I will repeat myself: If you gun shoots well heavy for caliber pellets, the shoot them! Be prepared to change springs every year or so if you shoot the gun often, but springs are relatively cheap.
Now, to put some perspective into the discussion: 10 grains and heavier are HEAVY FOR CALIBER 0.177"
12.5 grs. and heavier are heavy-for-caliber in .20"; 15.5 grains and heavier are heavy for caliber .22" and 22 grains are the border in .25" and all these are equivalent between themselves, they are calculated using the Sectional Density.
The other aspect is that you need to remember that, as Dimitri said, what counts is the sudden deceleration of the piston. THIS is the energy that gets transferred to the pellet (plus the little chemical energy of the oil's combustion), not the STORED energy of the spring but the kinetic energy of the piston. Which may not be the same.
If you think along these lines you will also see why a heavy piston is better to shoot heavy pellets, and/or why the dead-blow pistons have so much more energy available to give to the pellets.
In the end, the rifle is ONLY a machine. It has a sweet spot that depends on a lot of things, and YES! you SHOULD try ALL the POSSIBLE pellets! YES, Yes, Yes! ALL of them! You amy be surprised at how different one pellet of the same weight behaves when compared to another.
There are so many variables that the best thing to do is to simply look at all the published figures and come to terms with the fact that our guns will not deviate substantially from the others. We need to try all the pellets and figure out what does THAT particular gun likes or dislikes.
IMHO, the best way to tackle that task is to chrono the gun with different weight pellets; and based upon the pellet that yields maximum ENERGY, work in that region to find out WHICH of those pellets in that weight bracket are the most accurate.