The changing component of the magnetic fields that produce eddy currents can come from two sources: a relative velocity between the field and the target or change in the strength of the field itself. For a number of reasons the bulk of EC actuation research has focused on the latter mechanism. Time-varying electromagnets are easier to both analyze and implement.

However, two motors spinning magnets to create eddy-currents through moving magnetic fields may be able to achieve something that is much harder with electromagnets: attraction AND repulsion without a complicated scheme.

The motor-magnet actuator says to the plate: "come here"

https://www.youtube.com/watch?v=Jt2F4T5mMsQ

"Now go away"

https://www.youtube.com/watch?v=licok7Qot8o

Combine that with "sashay left and right"

https://www.youtube.com/watch?v=3cbUSCjhlJs

And you just may be able to dance with a spaceship.