Magnet coil cores, demagnetization power and Lenz delay.

[minnie]

    Oh dear synchro1.
                          John.

[synchro1]

This kind of "Magnet Positioner" from RWG'S Levitator kit could be powered directly by a D.C. motor attached to the screw. The motor would simply have to be mounted to slide along behind the screw between ridge rails.

This video by TK shows a D.C  motor reversing from a voltage divider circuit:

https://www.youtube.com/watch?v=SUsA-YuAtBU

Rotor acceleration increases from DLE, raising flux density and Ohmic resistance in the ferrite core. The circuit senses this and backs the magnet away from behind reducing flux density in the core. This balance should permit DLE acceleration to resume.

[synchro1]

A small push pull solenoid like this would probably work even better:

[synchro1]

There's a whole family of cheap "Electro-Magnetic Holding Solenoids":

[synchro1]

Look at this family of linear stepper motors: This motor positions the sideview mirror in your car.