The cube/vehicle/chassis would have it's normal payload as well as some type of driver to control the solenoid to simply pound the plate to push the space chassis in a direction. Getting the chassis to move in a particular direction can be done by a motor. Yes the whole chassis will move but who cares if both the chassis and motor moves as long as the chassis moves. Then strike the solenoid rod against the plate a few times (even if it's a hundred times) to push the chassis in the direction the solenoid drives against the plate.
There would be vibration issues and material fatigue of both the plate and the solenoid rod, and I certainly wouldn't expect this to be used on a large scale. but this certainly could provide a new way for cubist to nudge their cubes away the the earth.