You probably already know this but free floating rotors are supposed to move. They prevent brake surge that happens when rotors are warped. I would listen to your mechanic before some guy on the internet. Especially when it comes to brakes. Best to research the problem or lack of when facing a big expense like that. Mechanics are not always the most qualified. Ride safe

When I say "some guy on the internet" I'm just referring to myself. Lots of qualified people on this forum.