Welcome to falling down the rabbit hole of bingo...predicting which square a book will fall under isn't always easy, no, but as long as you think it'll work for a square or two, you can decide whether to count it for the square that's been called or use it for another square (and wait for that square to be called) after you've finished it. So it might get a bit messy...
So if I have it correct we can start reading any of the books on our list even if they haven't been called yet? Then we just mark off when they have been called and we finish the book? Was making sure I had read the rules correctly. Though I could be totally wrong.
Yeah, you can count books you started earlier than the call, but you have to wait till September 1st to start any. I'm not sure whether we can shuffle things around later, but I'm pretty sure that if the first square called isn't on your board, you can pick any of your books to start and just hope it'll be called soon so that you can mark off a square.