Jason - the problem is due to the internal limit switches. In a static situation, one limit switch is open and the other is closed on both actuators. When power is applied to the closed one, and the motor begins to turn, the open limit switches close. Now you have a potential feeback circuit when there are 2 motors connected.
The feedback is due to the induction of the motor and should not have anything to do with wire size. However, I am not an EE, so don't know this 100%. I know this is a typical problem with AC motors and feedback control loops in industrial applications.
Here is the email I got from Joeseph Turney at Zodiac Pool Systems when I asked about this problem:
"Also, if you have two actuators set up on the same switch and they're not adjusted to stop at the same time, the actuator that has already reached position will backup a little and continue to toggle until the other actuator is in position. Hope this helps!"