LED cube problem

I woke up in the middle of the night (which usually doesn't happen) with the thought that my idea of reversing the polarity of the LED in the matrix to double the number of LED I can control wouldn't work. I drew a small version on a piece of paper, and indeed: it doesn't work. There is no combination of control signals that will allow me to turn on only one LED. It's fortunate that I discovered this now, instead of after soldering the next layer of LED. I can still control the cube with 16 lines, but I'll have to use a matrix of 8x8 divided in 4 4x4 segments rather than using two 4x4x2 segments. There will be a switching issue, but at 20 MHz this shouldn't create a big problem.