First of all, it's an ordinary brushed DC motor, so the speed is simply controlled by the voltage applied to it, just like the motor in a cordless drill.
Exactly, that's why I want to know what kind of speed controller this is, and what kind of components it uses. Here's a picture, it's just one of those triggers for cordless drills.
I know most semi-conductor based electronics don't like overvolting that much, but the thing looks quite rugged and well made so I suspect it may get the job done.
Oh I think those are linear actuated potentiometers. Measure the resistance of the leads with the trigger depressed, and undepresssed. It might be something like a few megaohms undepressed and little to no resistance fully depressed. That way you can directly control the voltage going to the motor.