Probably not easily achieved with the way it is constructed, but your idea has some merit. A linear actuator of the motor driven variety could possibly fit in place of the coil, but does such a thing exist as a gear driven DC motor?How about this option, which would replace the solenoid with a small gearmotor driving a cam to provide the same displacement, but over a time of a few seconds, That could be nearly silent and not have much of an inrush, and consume much less current.
