Yes Caucasus is more brachicephalic in general. But certainly not to extent for G to be in front of a genetically distant groups such as O,P,R1a... It just looks unnaturally displaced from ME place of origin and much closer groups such as J and I.
Just to clarify myself:
I personally, think dolichocephalic skull is, when not in extreme form, probably more appealing to us, people of Europe, with somewhat eurocentric beauty model. This is not applicable to other cultures such as of Mongols, Huns Tatars... who favored this other form to its extreme following its own warlike skull types, even shaping them to look more broad and threatening.
But for me, and most of people I know, the most beautiful people are certainly not extreme dolichocephalic nor the other one, but just somewhere in between, maybe a just a tiny bit closer to dolicocephalic. This is probably what most of anthropologists from Europe thought about Caucasus people.
I am not a supporter of racial theory, nor anything such. I posted this just for reference.
Racial scientists, after discovering an intimate similarity between the skull shapes of Caucasians (primarily judged by Circassians, Georgians and Chechens, the most numerous groups), went to declare that Europeans, North Africans, Middle Eastern peoples and Caucasians were of a common race, termed "Caucasian", or later, as it is known today, as "Caucasoid".
Here is where I think you missed my point. HG G is a rare gene, and when it apears in Sardinia in 15 % or Turkey with 11% ( there are also 3.000.000 Circassians in Turkey), it looks like much and one is tempted using this rather small group of 15% to argue anthropology on behalf of 85% of other genes. I thing this is a big mistake.
As for Sardinia and HG I dolichocephalic connection,
Cephalic indexes map I have, shows I2 place of origin as even more brachicephalic than this of Caucasus, or at least similar, and this is quite true, at least in my experience, and my everyday observations.
Anatolian neolithic expansion with B type in not showing on the map, and it probably had no such impact. Actually this map would look diferent if Russians did not expand south, and it would connect Central Asia, Europe, and Anatolia, and Europe and Asia through north and Black sea, if we follow this map data.
http://www.theapricity.com/snpa/bilder/troe-map6a.jpg
http://www.theapricity.com/snpa/bilder/troe-map6b.jpg
My point is that when extrapolating antropological data for G, it is best to use counties where it reaches its maximum. And there is where your connection fails. The highest G is among least of brachicephalics, such as Circassians, while in much smaller numbers among strongest brachicephalic presence in Armenia. Georgia is somewhere in between moderately B., just proportionally.
So Turkey, Sardinia ... are hardly comparable to Caucasus in terms of G prevalence, and just not the places to look for HG G anthropological connections. Also I would use autosomal genes in addition, to clarify most of uncertainties.
So I agree that brachicephalic type prevails on Caucasus, but among G IMHO is found mostly in its moderate form, still brachicephalic though, so appealing to early European visitors, but can also be found, in smaller numbers, as a strong brachicephalic.