Quibble: "Men" does not mean head, it means front side or surface.
I have never heard of men-nage, but of course there are all sorts of names floating out there.
That means I am interpreting shomenuchi wrong as well then..
( I don't doubt that it is so, just didn't know)
Shomen uchi-uchi=strike, Men= head (I thought) and Sho= front
(In this context)
Strike to the front side of the head
I wonder what the literal translation is?
So, "strike to the front-side" for shomenuchi?
That would explain the confusion on the term for the head throw also.