but all point the nose to the sky until the airflow separates from the wing.
Not quite true, for example, if you fly a loop without a lot of power on and a little slow then at the top pull hard you can get the aircraft to stall whilst the nose is actually pointing down, the bit that confuses many with this is that though you are inverted, it is still a
positive stall.
This would be much the same as you shoving the nose down to do a negative stall, though I would suggest to achieve this you start by pulling the nose
up so the aircraft is decelerating, then start a gentle push to give a slight negative G (in this way you can get the speed well below the level stall speed), a little before the nose reaches the horizon again push hard and you might just get your negative stall with the nose down, if you try and just do it from level flight the increase in speed will probably defeat the stall.
This
Does of course need to be done in a suitable aircraft!