All you're doing is creating a bit of a tail wind, which the plane's engines will quickly over come.

Unless the pilot throttles back to intensionally not overcome the tree.

How about this, instead of slowly starting the tread mill (with the plane at rest), have it start suddenly/quickly with a jerk, like yanking the table cloth out from under a set table. The planes' inertia will keep it from moving backwards and the wheels will just spin on the tread mill while the plane stays motionless relative to the tree.