What force is causing the wind to move downwards at the top? There's something called "no-slip condition". Fluid flowing past a solid surface tends to stick to it. Hold your finger near water flowing from tap (flow should be very less), water sticks to your finger and runs down along it.
Similarly, in case of wing, air above it sticks to surface and flows along it till 'separation point'. The curvature of wings works as guide to air and throws it downward.
The understanding that "the wing is exerting a downwards force on the wind(above the wing)" in my opinion is due to ignorance of no slip condition.
"Bernoullis principle, viscosity, and pressure can all explain this, but how do we do this soley in terms of forces?"
In terms of forces: Air above the wing is deflected downwards by the wing. Hence by Newton's 3rd Law the wind must exert an equal and opposite force on the wing.
In terms of viscosity: You simply can't
In terms of pressure: The stream lines above the wing are being thrown downward the streamlines above them must move down to occupy vacant position, this causes a low pressure zone above the wing hence the lift
Bernoulli's principle: It's a myth, the assumption that fluid should flow faster above the wing to match the time required (to move pass the wing) by wind below the wing is invalid and lacks evidence. The correct way will be to use streamline curvature theorem. More about it