Thank you Pat, that's exactly what I had in mind.
Steve, I agree that the momentum of the system you have defined is conserved. My disagreement is the way the force is transmitted. I do not think that the air molecules that leave the wing travel to the ground.
We can see this clearly in the 2D case in the picture I posted earlier
Strealines are essentially a frictionless wall. By definition, the air flow cannot cross a streamline. With this in mind, it is clear that the air going past the wing does not really change in altitude much after it is downstream from the wing.
The 2D case demonstrates the effect of the bound vortex, so this example does not demonstrate the effect of the trailing vortices.