I've also been pondering this for years, so I'll take a crack at it.
I think that Bernoulli and Newton's third law are both at work in creating lift. When you consider the propeller blade (which is a rotating wing with typical airfoil cross section), it does NOT create thrust by ONLY creating a low pressure area in front of the propeller. If this were so, air behind the propeller would move forward to fill the low pressure area in front of the propeller. From experience we know that propellers move air rearward when producing thrust, and more thrust means more air moving rearward at faster speeds. The fan blade of a high bypass turbofan (another wing) produces thrust with very large movements of air. This illustrates that N3 is at work.
However we also know that Bernoulli is at work in the propeller because of the propeller tip (or wing tip) vortex, which is caused by high pressure air trying to move in and fill the low pressure area on the other side of the wing. We know this can only happen at the tip because the air mass is moving over the wing, and that the wing itself is in the way, blocking the rebalance of the pressures except at the tip.
I think that at very low angles of attack, Bernoulli is mostly at work, but as AOA increases, N3 increasingly does most of the work. I think this explains the shape of the AOA drag curve for airfoils. I also think this explains the AOA stall curve of airfoils. As the stall begins, lift starts to fall off as separation and turbulence begin, but the lift falls off on a curve. I think this shows that as Bernoulli falls away, some N3 remains.
I think Bernoulli adds efficiency to a wing. Even a barn door can fly with enough power, which confirms Genghis's theory of pretty flying machines. However there won't be much Bernoulli at work here, only N3. I think that Bernoulli is very energy efficient because it is only creating pressure differences. I believe N3 takes a lot more energy because with N3 you are not just creating pressure differences, you are moving air. Again, I think this explains the drag curve.
So to summarize, my theory is that at low angles of attack, Bernoulli is mostly at work. But at higher angles of attack N3 is mostly at work, and there is a transition from more of one to less of the other as the AOA changes.
Genghis, please way in as needed. Anyone else, please way in as I would really like to nail this one down once and for all.