BMatthews,

I don't think the essential aspects of the different explanations are mutually exclusive. The suggestion that the sum of the surface pressures (to be more precise, the surface "tractions"... including shear/tangential as well normal forces) isn't equal to the net aerodynamic force on a body is difficult to support. The statement of equality between the surface tractions and the net aerodynamic force is really more of an "identity" than explanation. The interesting question is how/why the motion of the air around a body results in the forces on its surface. Explaining lift in terms of "circulation" doesn't exclude the possibility that lift results from momentum transfer, and vice versa. And certainly neither of those explanations contradicts equality between the sum of the surface forces and the net aerodynamic force.

The underlying physics of fluid flow are pretty well understood. The complication in solving airplane-scale problems has more to do with shortcomings in book-keeping than in understanding the forces at work. I think a reasonable analogy would be that it is possible to have a good understanding of how humans interact with each other financially, but not be able to reliably predict the behavior of a large scale economy. There are so many moving pieces and there is so much interaction that keeping track of what's going on is the real challenge