I'm really surprised that this is such a hard thing to fix. I had a similar problem where a electric motor from an airsoft gun was causing interference in the boards inside of hobby servos. This interference would cause them to jolt each time the motor made the gun fire. This was simply solved however by adding 2 capacitors spread along the power leads going to the gun and maximizing the distance between the gun motor and the servo. This is the same kind of thing but now dc motors are interfering with an analog video feed instead.
Even after reading all of this, I still don't know if the problem is RF interference, or drastic voltage drops/spikes. Gotta know that first to be able to move forward...