@Socratic.Fanatic, are you trying to kid a kidder? You know me... I love speculations. But I don't insist on speculating "what if" on every semantic curiosity.
Having a noose put around a captive's neck was a known practice in the middle east, which is how the Templars came to practice it. And I'm confident there are other examples of it long before the Templars. In contrast, there is no known example of putting a coil of rope on someone's head to mean anything.
The Hebrew proposition for on one's head is an implied meaning... one which was poorly grasped by the scholars employed by King James.... just as the Breeches Bible erroneously described the plant-based garments fashioned by Adam and Eve as breeches, rather than as more of a loin cloth made of leaves.
@Socratic.Fanatic, this is now your cue to describe the possible nuances of a little discussed possibility: what if the scribes of Genesis literally believed that Adam and Eve made trousers?