measure your box and cut some masonite slightly smaller. i think i went 1/4" smaller in both dimensions, making the masonite piece 1/8" smaller than the frame exterior all around. same cutting technique here as with cutting the chipboard strips.
before i screwed my masonite on, i ran a strip of weather seal all around the back. this will prevent light from leaking out of the back edges and distracting from the beauty of whatever you stick in the front of this thing.
the masonite back is going to give your box strength and shape. make sure that your box is square before you put in too many screws. to make sure the box is square, measure from corner to corner in both directions. if the measurement is not the same, your box isn't square!