I doubt you could put enough weight onto a simple pushrod to move the CG far enough even if it was literally a brick. The travel is too short.

You'd need a long threaded rod and motor to turn it and limit screws to shift a smaller weight pretty much from one end of the model to the other. Remember that mass times distance is the equation and to keep the overall flying weight down you need a lot of travel.

Or if the jack screw deal is too slow a tube with a pneumatically driven weight with controllable locks at each end would be quicker.