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I get that the rotor moving is likely causing a rub but why is there a noise when the brakes are off, that is reduced when they're on? It's like the pads are loose and maybe sitting crooked and when the pistons move in, they straighten the pads out so they no longer touch the disc.
I need a closer look at what's going on. Upgrade time...
hippy-
When I've had this problem the rotor was a bit bent, and squeezing the brake just lightly touched it to the rotor evenly through its rotation which stopped the 'tsk tsk'. I realised when it occurred to me that the 'tsk tsk' would be more frequent if it was the pads, on mine it was basically once a rotation, and as the pads stay still and the rotor rotates, it made sense it was the rotor having a kink. You can true a rotor with the a spanner.
spotter
You got to bend the rotor not the pad