Think of it like this Curtis.

When I jump into my 152, start it up and proceed to taxi I have to gun the throttle to get it moving.

Once its moving I can ease off the throttle because momentum has taken hold.

To overcome static rest I had to make the engine work more.

This is why terms and common agreement of the riddle is important. I am assuming zero thrust, zero wind, speed of conveyor matches GROUND SPEED of airplane (relative to a fixed point on the ground - not the conveyor), the conveyor matches precisely the moment and force of forward motion of the plane

Still with me? That is our starting point.

The plane will not move, the conveyor will hardly move. You have to think of it at the very genesis of actions and reactions taking place and freeze frame that moment in your brain i.e. thrust creates forward motion - that motion is calculated with a ground speed - that ground speed is matched with an opposite conveyor speed - at that very point ground speed is still zero.

My only guess is that the disconnect is something with the ground speed - maybe you are assuming the treadmill speed matches the wheel speed...I am saying the treadmill matches ground speed relative to a linear point in space not related to the treadmill or the speed of the wheel over the treadmill.