I love the cube idea though, I think it would bypass some of the luck in the initial placement and add strategy in it's stead

For the numbers you could use X, Y, and Z axis with corresponding numbers like math. like 132 would be 1st line on the x axis, 3rd line on the y axis and 2nd on the z axis. If familiar with the system at all you would be able to find the stuff really fast and easy. sorry if this idea has already ...