String pitch isn't determined by the stretch, its determined by length and tension.
Indeed and by pushing the string towards the side you are lengthening the trajectory it follows from bridge to nut, which means the string is elongated thus raising tension.
A lower flexibility string requires more elongation to raise the same amount of pitch.
ANY bend will require the SAME amount of end force. The difference is over how wide a distance. .
you are quite wrong here,
As you bend a string, the angle of pull with respect to your bending force changes (force - along the fret vs force - along the neck), at very shallow angles this means that the force exerted on your fingers goes up almost linearly. Because of the angles there is also a slight difference in force when bending near the nut, where on the nut side the string angle is much steeper, compared to bending at the 12th fret.
On top of that the elongation causes the string stress to increase, there would be no pitch increase without it, and you might feel that as well but the effect is less pronounced. Bending up a full step requires about 12% extra stress. You can replicate this by bending up, then pulling up on the trem simultaneously.
meaning that the springs are then applying DISPROPORTIONATE FORCE to the string YOU are holding, as it has more tension on it than the others at that point..
this indeed happens slightly, see the trem pulling above, but the effect is not as big as the effect of the angles, IE. the extra force coming from the wider bend. The extra tension in the string is still 12% for a full step, this is no different from a fixed bridge.
As you mention the other strings DETUNE as the trem lurches forward, but only by several cents, not a half step let alone a full step, so the decrease in tension is actually very small (much smaller than 5%).
Please don't make baseless assumptions about my playing. I bend to pitch.
fine I believe you, this was never about your playing, I´m sorry that you took it that way.
But your assumptions and explanations are incorrect and it could only mean your fingers are lying to you, in stead of your ears. As I explained before, in the particular cases you've mentioned you will require more force to bend to pitch (as it requires a wider bend)
If this weren´t the case even the tiniest of fingers could bend up and octave, provided the fretboard was wide enough.