That sounds intriguing, excellent idea!
I'm not exactly an expert with quaternions yet, but I do know the basics (x, y, z define an arbitrary axis around which we rotate by w). How does dividing the other components by the largest one (x, y, z, with w or without?) leave me with a 4 cube division? I don't understand that very fundamental step!
The 544 angles are 32 yaws and 17 pitches!