The idea I have is that, on being triggered, each hard drive would start reading/clicking and then die out (doing less and less). This could be triggered over and over.
You can control the VCMs easily enough with a motor driver chip or even just some transistors and PWMing it.
They're what make the head move and make it 'click'.
Controlling the motor itself would be more tricky but most hard drives will spin up the motor even if nothing else is connected apart from power so you could control the power to the HDD with a transistor and just turn it on when you want the motor to spin.