Hel,
I have astigmatism, which means my cornea has a strange shape that changes the way light enters my eye. It's pretty common, even if sounds odd.
The thing is, if I diverge (this is all my theory, I don't know this for a fact, just and educated guess) light doesn't go in the right way; I get a blip page, but the words look blurry, like my vision is failing.
If I take my glasses off and diverge, it's fine: blip page, and the words are still legible. I guess I want it entering my brain in clear state.
The nearness of the book, however, is more of a thing of, if your eye took a picture right now, could you see all of the text in front of you in good focus (albeit with a blip page)? You want it far enough so that while diverging the eyes, you can see all four corners of the book.
Since I take my glasses, I have the same problem as you (ie - the book is close enough that I can read it, but now it's not far away). It wasn't too bad, because I've been diverging my eyes my entire life (the strange games we play as children) and I just compensated by diverging far enough that I can get all four corners in my field of vision (top and bottom is harder, so you have to concentrate and really stare through the center of the book now). I'm so close the pages almost hit my nose, but I still get the double pages (I'm that blind).
Hope that helps. =)
-Ramon http://razor.ramon.com ("RSTLR..P" "Good good...now, try reading the chart without your glasses, Ramon." "Uhm...okay..." "What's the first line you can read?" "Actually, doc, if I didn't see it before with my glasses, I would have no idea that the big letter on top is a '3'." "Ramon, it's an "E"." "oh.")