There is nothing wrong with your idea, it's called a 2.5 way setup, and you'll have to use a proper inductor to keep the frequency response in check at the higher frequencies. The only thing I would worry about that is the inductor not rolling frequencies off enough to eliminate breakup modes. The way to fix this is to just mount the woofer on the front of the box instead of the back. As far as pushpull goes, it may not be a good idea with your woofer running up to 600 Hz or even higher.

Adam