Regulating Voltage at High Current
Doing this with a linear regulator is possible but you'll need a sizable heatsink and probably a fan to dissippate the 42W wasted in the linear regulator. 42W comes from 7 circuits dissipating 6W each. 6W comes from producing 9V from 12V at 2A.

I'd definitely consider a buck switching regulator. It's likely to be +90% efficient and would therefore be only dissipating about 10W in total. Reducing the voltage to (say) 8V or 7V won't make the dissipation any worse either BUT if it were a linear regulator, the power dissipated would be approaching 70W.

What sort of buck regulator? I would consider using 7 of them like the linear approach but i'd probably go, in the end for 4 x 5A regulators with each driving two motors and the final one driving the seventh.

What about the LT3976: -



The 1M ohms resistor and the 110k resistor set the output voltage and this of course can be chosen to give 9V. This device is not a synchronous device and therefore it's efficiency could be higher if it were BUT this would meet the requirements.