It's finished. The redstone is a little glitchy, the last dispenser in line doesn't always fire, but it works.
The only access is via the nether. From spawn, follow the signs to the north red level path. You'll find signs to the Ice Palace from there. The ice tray is on the roof, which is covered in half blocks so mobs won't spawn. Empty the tray, then push the button. You'll get 5 stacks + 15 from a full tray. Please completely empty the tray before you push the button.