BTNP with a snatch grip might be too hard on the shoulders, I did it standing and I was fine. But you could do it as a push press?
The push jerk as Fazc says has a double knee dip. First dip is like a push press, then the 2nd one is where you "catch" the bar as you dip under it.
With the BTNP press + overhead squat, did you mean the snatch balance?