PWM 12V DC motor using lower supply voltage for lower speed operation?
Rather than saying "the very low end of the PWM" you should state the RPM or percent of full speed at which you are attempting to operate. Operating a motor continuously at a very low speed can cause it to overheat. The motion of the rotor helps to move air through the motor for cooling. When the rotor is moving very slowly, the cooling is not as effective.

The speed controller will also have difficulty with maintaining a steady speed at a small percentage of full speed without tachometer feedback.

If you never need to operate at full speed, the best solution is to reduce the speed a little bit with a belt and pulleys. If you only need to operate at full speed occasionally, consider a stepped pulley arrangement. If neither of those alternatives is possible, you may need a tachometer, a closed-loop speed regulator and a separate fan or blower to cool the motor.