The control unit is normally the problem.

In this case though it might be alright run from 12V rather than 9.6V but don't blame me if it melts down.

And no, a transistor won't work if it's terminals are reversed.

I have run r/c boats (surface drives, etc) on very high voltages. In my case I used ESC (electronic speed controllers), although on occasion I did use mechanical arm type that was rated for it. I went as high as 36 volts in some of my projects.

What type of speed controller are you using? If ESC, simply use one that is rated for the higher voltage. If mechanical, I am thinking that the ceramic resistor may burn out quicker. In actuality, 12 V is not that much more voltage to be concerned about in this instance, from my experience with r/c.

I believe this is simpler than you are making it out to be. Good luck & have fun!

EDIT: BTW, if you are looking for a speed increase (top end?) gearing would probably be the way to go. I would also recommend installing a heatsink on the motor case, they can really get hot. I have also swapped out armatures in the standard 540 size motors for better performance. That is probably the best solution to really get that motor cranking, even using the standard size battery pack.