How has kephalē (κεφαλὴ) been used in lexicons?

In my last post in this series I tried to summarise one of Wayne Grudem's articles advocating for κεφαλὴ to mean "ruler" and not "source". In that last article Grudem made reference to the main Greek lexicon and was a bit unhappy on their definition of κεφαλὴ. He said:

The omission of the meaning “authority over” from the Liddell-Scott Lexicon is an oversight that should be corrected (but it should be noted that that lexicon does not specialize in the New Testament period)

and later:

...the evidence we have cited above showing around forty examples of this meaning indicates that the omission from Liddell-Scott must have been an oversight that we hope will be corrected in a subsequent edition.

A few years after Grudem made these statements, he sent his article off to the editors of the LSJ to see what they thought. P. G. W. Glare got back to him.

I remember once hearing that Glare had been at Oxford for about 40 years studying languages and in that time he had taught no subjects. He has been a straight researcher of languages for 40 years. In his time at Oxford, P. G. W. Glare has edited the Oxford Latin Dictionary as well as the LSJ's Revised Supplement. I think it is safe to say that this guy knows Greek (and Latin) quite well.

Anyway the start of Glares' response to Grudem went like this:

Thank you for sending me the copy of your article on κεφαλὴ. The entry under this word in LSJ is not very satisfactory. Perhaps I could draw your attention to a section of Lexicographica Graeca by Dr John Chadwick (OUP 1996), though he does not deal in detail with the Septuagint and NT material. I was unable to revise the longer articles in LSJ when I was preparing the latest Supplement, since I did not have the financial resources to carry out a full-scale revision 

I have no time at the moment to discuss all your examples individually and in any case I am in broad agreement with your conclusions. I might just make one or two generalizations. κεφαλὴ the word normally used to translate the Hebrew ראש, and this does seem frequently to denote leader or chief without much reference to its original anatomical sense, and here it seems perverse to deny authority. The supposed sense ‘source’ of course does not exist and it was at least unwise of Liddell and Scott to mention the word. At the most they should have said ‘applied to the source of a river in respect of its position in its (the river’s) course’.

Glare also ends his letter suggesting that applying the meaning of "pre-eminence" to κεφαλὴ is also quite unsuitable. I think that kinda settles the argument. Grudem published that letter in another long article in 2002 reviewing more uses of the word κεφαλὴ which I don't feel like I need to summarise, the link to the full pdf is below.

I also happened to get my hands on BibleWorks 8 and in that it has a few lexicons other than the LSJ. Below are what they have for κεφαλὴ.

Friberg's Analytical Greek Lexicon

1. literally, of a human or animal head (MT 6.17); 
2. figuratively; 
1. metaphorically, of Christ as the head of which the church is the body (EP 1.22); 
2. of persons, designating first or superior rank head (1C 11.3); 
3. of things uppermost part, extremity, end point; of buildings keystone, capstone (MT 21.42); 
4. leading city, capital (AC 16.12)

Gingrich Greek NT Lexicon
head:

1. lit. Mt 5:36; 8:20; 27:29f; Mk 6:24f, 27f; 15:29; Lk 21:28; J 13:9; Ac 21:24; Ro 12:20; 1 Cor 11:4f, 7, 10; Rv 10:1; 17:3, 7, 9; 18:19; 19:12.
2. fig.
1. head denoting one of superior rank 1 Cor 11:3; Eph 1:22 ; 4:15; 5:23; Col 1:18; 2:10.
2. head as extremity, end γωνίας cornerstone Mt 21:42; Mk 12:10; Lk 20:17; Ac 4:11; 1 Pt 2:7. Capital or frontier city Ac 16:12 v.l. [cephalic] [pg 108] 

Louw-Nida Greek-English Lexicon of the NT

1. head 8.10 - In some languages it may be necessary to distinguish clearly between the head which is still a part of a body and a severed head. It is this latter meaning which is obviously involved in Mk 6.25. In rendering 1 Cor 11.4, it may be important to indicate that the covering is not one which is designed to cover the entire head including the face, but only the top of the head. The same applies, of course, to 1 Cor 11.5 and 7.
2. superior 87.51 - (a figurative extension of meaning of κεφαλὴ, 'head,' 8.10) one who is of supreme or pre-eminent status, in view of authority to order or command - 'one who is the head of, one who is superior to, one who is supreme over.' Eph 4.15; 1 Cor 11.3.
1. κεφαλὴ γωνίας - cornerstone 7.44
2. κατὰ κεφαλῆς ἔχω - have one's head covered 49.16
3. τὴν κεφαλὴν κλίνω - lie down to rest 23.83
4. ἐπαὶρω τὴν κεφαλὴν - have courage 25.160

(I didn't bother expanding on the meanings in the sub-categories)

Thayer Greek-English Lexicon of the NT
the Septuagint for ראש; the head, both of men:  Matt. 5:36; Mark 6:24; Luke 7:38,44 (Rec.),46; John 13:9; Acts 18:18; 1 Cor. 11:4 ; Rev. 1:14; 4:4, and often; and of animals: Rev. 9:7,17,19, etc.;
on the phrases κλίνειν τὴν κεφαλὴν, ἐπαὶρειν τὴν κεφαλὴν see κλίνω, 1 and ἐπαὶρω;
on the saying in Rom. 12:20, see under ἄνθραζ.
Since the loss of the head destroys the life, κεφαλὴ, is used in phrases relating to capital and extreme punishments:  so in to, τὸ αἷμα ὑμῶν ἐπὶ τὴν κεφαλὴν ὑμῶν (see αἷμα, 2 a., p. 15{b}), Acts 18:6, and similar phrases in classical Greek; see Passow, under the word, p. 1717{a}; Pape under the word, 3; (Liddell and Scott, under the word, I. 3 and 4).
Metaphorically, anything supreme, chief, prominent; of persons, master, lord: τίνος, of a husband in relation to his wife, 1 Cor. 11:3; Eph. 5:23; of Christ, the lord of the husband, 1 Cor. 11:3 (cf. Buttmann, 124f (109)); of the church, Eph. 4:15; 5:23; Col. 2:19 (cf. Buttmann, sec. 143, 4 c.); τοῦ σώματος τῆς ἐκκλησίας, Col. 1:18; πάσης ἀρχῆς καὶ ἐξουσίας, Col. 2:10; so Judg. 11:11; 2 Sam. 22:44, and in Byzantine writings of things:  κεφαλῆς γωνίας, the corner-stone, see γωνία, a. ((From Homer down.))*

All of these lexicons seem to not include "source" in any variant meaning and only Louw-Nida suggests that "pre-eminent" maybe used when dealing with someones status. This site has a quick summary of some of the above lexicon definitions in case you think I am lying.

To me it seems that κεφαλὴ means "head" and is used to metaphorically to denote someone who has authority over someone else, like the head-honcho or a big-wig.

Works Cited

Grudem, W. A. (2001). The meaning of kephalē ("head"): an evaluation of new evidence, real and alleged. Journal of the Evangelical Theological Society, 44(1), 25-65. 2002 [Full PDF here, this contains the letter in full by P. G. W. Glare on page 188]

Other works I could have read but didn't, due to time

Fitzmyer, J. A. (1993). Kephalē in I Corinthians 11:3. Interpretation, 47(1), 52-59. Retrieved from EBSCOhost.

Polidoulis Kapsalis, M. (2004). St. John Chrysostom's interpretation of Kephalē in 1 Corinthians 11:3-16.Greek Orthodox Theological Review, 49(3-4), 321-356. Retrieved from EBSCOhost.