All of the docs on the Adafruit motor shield warn that it's just for low current motors. Motors on 12 V linear actuators need something more like 6 amps at 150 lbs, which is way beyond the motor shield. I'm using this Progressive Automations actuator. The red and black lines are the drive current. The other three are a position potentiometer with blue connected to the wiper.
Enter the Polulu 18v15 motor driver: http://www.pololu.com/catalog/product/755. It comes with the screw terminals and capacitor loose. I added the capacitor a little offset to make sure there's still good airflow to the chips for heat dissipation. Polulu says it's good for 15 amps without a heat sink, so it may be overkill.
It works about the way I expected, except that the +5 volt line is an OUTPUT that can provide a few milliamps for additional circuitry. Initial tests set PWMH high for full speed and changed direction with 5v and no connection other than the LED.