As far as I understand, you don't actually change the grip. I grip with the bar in the "heel" of the hand the whole way. If you're changing grip, you can't really do the whole squat-to-press thing in one dynamic movement. It's not the same as a front squat or a clean.. it also doesn't need to be because the weight is comparatively light.
However, I'm a bit of a beginner too, so I might have it wrong.