Both sides equal when pressed, and neither corner affects the opposite corner any more than the other one does when pressed, if you see what I mean. You might need to read that several times ;-)
The unequal settling doesn't happen if the brakes are off.
And it doesn't happen to the same degree once I've released the brakes and re-applied them, then put it into drive / back into neutral. So presumably some latent energy is being stored (like a coiled spring) at the point of stopping the car, until the brakes are released, at which point the energy is dispersed.
Having just re-read the above, I'll be amazed if you can understand any of it. Time for bed.