I'm too lazy to do your sketch, but you get the same effect by just raising your arms as you do holding the rope above your head.
This is the image I've just posted over at Sailing Anarchy (for the one or two of you who don't visit both sites). As people have been trying to explain, while your feet are on the hull there is no advantage in putting the righting rope over the hull except it is easier to hold, however, at some stage you come off the hull during righting and this is when the over the hull system becomes superior.
Using a righting pole is different as it allows you to move your weight away from the hull immediately.
That's true. But when you come off the hull I suspect that you are already done and it might even be better to have less lever arm, so that the boat comes out slowly