You can't assume people to understand the Japanese terms (such as Ogoshi, Koshi Garuma). What's wrong just to use "hip throw" and "head lock hip throw"? Even if it may only take me 10 seconds to Goggle it. But for 1000 MT members, that will be 10,000 seconds.
It makes sense to use under hook and use your palm to push the back of your opponent's head when you execute hip throw. The head lock hip throw does not make sense.
The hip throw require a "lift' motion. The head lock is a "sideway" motion (not even a downward motion). It makes no sense that you try to lift your opponent with your hip, at the same time that you press his head sideway with your head lock.
If you do head lock correctly, your opponent's spine will be bent side way. This side way bending spine won't work will with hip throw. If you don't bend your opponent's spine side way, your head lock won't be effective.
The horizontal circular head lock motion won't work will with the vertical up and down hip throw motion.
In the following clip, since A's head lock is a vertical up and down motion, B's free left hand can push A's head lock right arm forward and let B's head to slide off A's head lock. But if A's head lock is a horizontal side way motion, it will be much harder for B to escape out of A's head lock.
Here is a correct head lock. It's difficult to apply a hip throw from that position.