nik,
I had a look at the document last night, but I was unsure what was actually needed: it seemed to be one layer with a number of separate paths with many Anchor Points.
Rethinking, and trying to remember/deduce what was actually in it, it may be a matter of deleting the Clipping Mask(s), then selecting a white path and Select>Same>Fill Color, then delete all of them (I remebered it as black paths with nothing in between, but the parts in between may have formed white paths, as from an Image/Live Trace without the setting Ignore White).