Shado, how is a spinning treadmill jet thrust? There is nothing in your scenario propelling the skateboard forward.
FYI, I know you were kidding in your first paragraph about a prop vs. a jet, but I just want to get it out in the open, lift is not created by the force of jets or the wind from a prop, it is created by the flow of air over the wings caused by forward motion of the plane or an air mass moving around the plane. In theory, given a strong enough headwind a plane can "hover" off the ground. This is why it is preferable to takeoff into the wind and land with it (
Point 5).
Although it is true the reversing speed "runway" will make it more difficult to takeoff, it will not hinder it completely.