Atkins is BY FAR the best book for USNCO. However, you might be in a time crunch to read all of it in the next two months, and it should mostly be review if you already know all of the AP Chemistry curriculum so you might feel like you're wasting your time. If you're going to read anything though, read Atkins instead of Zumdahl.
Also, it would probably be more beneficial to just take practice tests. There's a lot on there that you'll learn only by doing problems and isn't addressed well in textbooks, such as qualitative reasoning and a few other points. Also, in my opinion USNCO is not nearly as hard as USABO - I'm reading for it now and there is much more content that you have to be responsible for to do well. If you understand your concepts and can solve calculation problems with a scientific calulator, then at least making the National Exam (and possibly even earning High Honors) should more or less be a breeze.