To the OP, why are you doing this exercise? Is it a sports-specific thing or what? Don't get me wrong, it seems like a nice lift. I hope you aren't replacing your normal squats or cleans with it, though. This lift is limited by how much you can push press.
I think if I were to try this I would go with an overhead squat. i.e. after the initial push press, keep the bar over your head, then squat.