slow down ice melting in water
Unfortunately there isn't much you can do to slow down the melting of the ice-water slush besides insulating your container. If possible, you can enclose the wooden box in styrofoam to prevent heat from entering the system. 

Another note you should keep in mind is that the water in the slush speeds up the melting of the ice. A better scenario would be to keep a large (minimized surface area) block of ice in one container, and the slush in another. Use an ice pick to break up the block and add pieces to the slush as needed.