Don't know if you're still listening, but...
You actually are headed in the right direction.
I'm not sure what you mean by "the reduced pressure in top face of wing is discounted", but will do a best guess.
With all due respect to CuriousOne, the "Push air down Newton Reaction lift" explanation is oversimplified and I believe misleading you to think this "push air down" is something only occurring at the lower wing surface.
The fact (true science) is that a larger amount of air is ""pushed down"" from ABOVE the wing (compared to below)! Yep.
What the "Newton Reaction" story omits it the very pressure difference you mention. There is indeed, a lowered pressure above the wing (pushing down) and an increased pressure below the wing (Pushing up).
The DIFFERENCE in those pressures over the wing's area is the lift force, the WHOLE lift force and NOTHING BUT the lift force. [that last part is actually false, but it sounds good and I'll explain]
As you described, the upper surface is, in essence, "running away" from the air above it. This is what lowers the pressure. In addition, you also realized that it also has the effect of creating some of the down-wash and this is also TRUE.
The lower surface (at a noticeable, moderate Angle of Attack) is obviously "advancing" on some air and this is pushing it out of the way by the fact that a push is in increase in pressure.
The pressure difference between top and bottom over the wing area is the upward lift force (Wing loading).
We also note that this increased pressure under the wing pushes air away from it in all directions. That pushes some air FORWARD ahead of the wing. This creates the up-wash ahead of the wing and because it also wants to get to the lower pressure above it moves slightly upward too. Yes, there is movement of air away from the wing before it arrives.
It also pushes down on the air further below which contributes to the down-wash behind the wing.
It also pushes air around the tips.
The fact is that it was Euler, not Bernoulli that realized that it was pressure gradients that accelerate the air in all cases. Pressure differences between two regions are the cause for the acceleration of air from the higher pressure region to the lower pressure region.
SO, we see that the pressures around the wing do two MAIN things: They push UP on the wing AND they push DOWN on some air. Therefore, the Newton Down-wash satisfies Newton's Third Law, but that doesn't CAUSE lift. It is something caused by the lifting-pressures and also satisfies Good-Old Newton-#3.
P.S. The thing I said was wrong about "nothing but the lift force" was the fact that those same pressure ALSO cause ALL OTHER accelerations if air around the wing.
P.P.S. I must add that the "faster air on top" thing is because the pressure ahead of the wing is full atmospheric pressure, but above the wing it is lower, so, that air ahead of the wing pushes (accelerates) the upper air toward the lower pressure region and the trailing edge.
There IS such a thing as "negative pressure". We also call it "partial vacuum", or just "vacuum' for short. It is simply pressure below the ambient pressure.
This is common terminology in various industries. The manifold pressure gauge in a piston aircraft measures this partial vacuum and it is still called just 'pressure'. It is absolute pressure.