Your example does not work at all.
I think it does.
Maybe I should get one source of confusion out of the way, by saying the "zero" angle of attack is the angle of the airfoil that generates no lift. In that it differs from any other angle of attack definition by a constant angle it's just a convention as to the zero you measure from.
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?
Yes, it does. For "sensible" values of alpha, lift is directly proportional to alpha.
And what happens if you start from zero degrees and you go to two, that's infinite acceleration to the stars now.
Zero angle of attack -> zero lift. Two degrees angle of attack, yes, the lift has increased "infinitely". You'd never be flying with angle of attack of the main wing though, you'd be accelerating towards the earth, because zero angle of attack -> zero lift.
Keep in mind that when dealing with dynamics, you are dealing with derivatives, not with static values.
The derivative of lift with respect to alpha is almost dead-on a constant value, reflecting their linear relationship, up to near the stall.
If you'd rather use a different definition of the angle of attack, say based on the chord, then define another quantity as the "angle of attack minus the zero-lift angle of attack". The analysis works just as well.
I have to say, it's not my treatment - it's John Denker's. I'm curious to see if you can fault it though.