Yeah, the upper wing surface has more area than the lower, but it acts as a constriction to the air flowing over it. A neat demo I found in a WWII Navy aerodynamics manual has you hold a spoon lightly, curved side toward running water (the kitchen sink works good). As soon as the spoon contacts the flowing water it's "lifted" into the stream. Kinda neat.

well, when you deal with 2D airfoils, there is no area. what the area is referring to is like a pipe, as you said.  What bernoulli basicly says, take 2 airparticles, they start at the leading edge, they split, one goes up, one goes down.  They have to meet at the trailing edge at the same time (they dont in reality, but you arent there yet.  So lets pretend they do).  In order for this to happen, the top particle must accelerate to cover a greater distance in the same time the lower particle covers it shorter distance.  Because the air going over the top surface of an airfoil is faster, there is a lower pressure on top compared to the bottom.  Lift is generated.  The airfoil is literally sucked into the air.

I think you are trying to combine too many different theories.  You never talk about areas with 2D airfoils.

On edit:
The Books you need are
Aerodynamics for Engineers
and
Fundamentals of Aerodynamics -- Tipler (I think)

and if you like, I can dig up my old homework assignments from Low Speed Aero and send you those and the solutions.  Hell, I may be able to point you directly to all the lecture notes from that class

What book are you using?

Edit:
Never look at the engineering aspects from a pilot's standpoint and vice versa.

Think of the air around the wing as it is motionless.  It exerts 1 atm of pressure.  The constriction example as used is, like you stated, the flow of water through a garden hose.  If the hose is not running and the water stands inside the pressure is even all around.  Then the hose is pinched, until flow is induced no change in pressure at that constriction inside the hose.  Well the upper and lower wing surfaces actually pinch the air around them against the atmosphere.  Thus a constriction.  When the airfoil is moved to induce airflow across it, viola!  Lift!

Also air is, for this exapmle, considered a fluid.