Can you give more detail? It seems clear that it is in fact the angle of attack delta that is the key, as described above
Your example does not work at all. Let's assume that instead of starting from 3 degrees you start at 1 degree. You pitch up two degrees so now you have 3 degrees, do you really believe that suddenly the wing produces 3/1 or three times as much lift than it did before? And what happens if you start from zero degrees and you go to two, that's infinite acceleration to the stars now. Keep in mind that when dealing with dynamics, you are dealing with derivatives, not with static values.