mmm. You're probably going about this slightly wrong. It looks to me like you're adding too much detail to the sub-d mesh anyways. Also, sub-ds cannot do sharp 3-plane (like for a cube) corners (I've tried, for a number of reasons).
What I reccommend is actually making the thing in straight poly (at least, from what I can see so far), and then just beveling/smoothing the edges that need to be rounded.