TL

”Do people want to dispute that kephale as translated in the LXX does not denote some sort of authority? This might be helpful as it is a significant primary document in understanding this word.”

The LXX is not the only source of understanding the use of kephale. And also you appear to be using it backwards. The point of the LXX is that when rosh was used in ways NOT about authority, that is when they used kephale in the LXX. And kephale has not been found to be used in the sense of authority.

”It seems like people are skirting around the issue that kephale is understood to mean authority both in biblical and other ancient greek literature. Is this a fair presumption?”

This is actually not correct at all. If you would read the links and the extensive research of McCarthy you would see that in fact the opposite is true. Kephale is NOT used to mean authority in metaphors. The primary meaning of kephale is the head on our shoulders. It may mean primary, preeminent, foremost, source, origin and other similar in metaphors. All those things are relative to what an actual head on a body could be considered. But people do not consider their physical heads, their authority. We are our own authority, our very person and we live in a body.

With all of the lengthy discussion in Christiandom about this, Grudem ended up with only one example in history to support his theory of head meaning authority. That was : ”the king of Egypt is called “head” of the nation”. But it has easily been pointed out that statement did not mean that the king of Egypt ruled, controlled, directed, etc. the other kings. What it meant was that the King of Egypt was prominent, he stood out among them as a physical head stands on top of the body.