You still didn't explain where the air moving over the wings to provide lift comes from. The engines simply hold the plane in place on the treadmill, assuming the plane is not moving forward relative to a ground observer. Engines provide thrust which is forward movement. We've already established in our model that the plane is not moving forward to a fixed observer - i.e. someone not on the treadmill.

To look at it from a different angle, if you put an airplane on a fixed runway with the highest friction wheels available and put a huge fan in front capable of moving the air over the wings at take off speed, the airplane would take off. It would have zero forward movement relative to the ground observer, but it would have sufficient air flowing over the wings to generate lift. Thrust does not provide lift. Thrust provides forward movement through the air.