I can't visualize it myself, all I do is remember which note is my root and from there construct it around the m3 and b5s for that note and the one above it.
Anyway, the way I used to see it is that whatever you play, 2/3 of it is in diminished, so as long as you stay 'somewhat diminished' you can just say "Mmm, nyyyuuuessss, the diminished went quite well there, but I didn't want to stay *too*... inside the box, *arrogant fake British chuckle*..." and people will think you're an artsy-as-fuck multidisciplined genius.
EDIT: Steve, is there any way you could loop the heavy part of that (without the quieter intro part) to give the less-sporadic among us (read: me) more time to develop ideas before cutting a solo? I'll still put it over the 52 second bit, I'd just like to figure out this one little part that just doesn't squeak in right.
Jeff