do I need an extra motor control board
You will need some kind of external hardware for the motors, if you want to control speed and direction then one of the H-Bridge shields would be a good choice.
I see places that say that with the servo library I can control 12 servos but, the documentation says it's not that accurate with more than 2.
Are you looking at the documentation for the Arduino Servo Library? The arduino library is just as accurate with 12 servos as 2.
And, it seems the servos want very short pulses, while motors need long ones for PWM, making it harder to share timers
The servos and motors do not share the same timers. On a standard Arduino board you can control the speed of up to 4 motors using analogWrite while controlling up to 12 servos.