A car hoist such as http://www.bendpak.com/car-lifts/four-post-lifts/ uses an ingenious mechanism to simultaneously lift 4 corners without having a bulky winch. There's an hydraulic cylinder hidden under one of the runways, In your case, this would be a linear actuator from a company like Firgelli.
To get extra lift without a long actuator, run all the cables from a fixed point over a pulley on the actuator. Then you can make the vertical travel twice the travel of the actuator.
There's lots of machines out there for storing stuff off the floor. It should not be difficult to buy the main part of the mechanism already built for you.