The more Balkan-shifted Csokorgasse group, which was dominated by E-V13, had some elite burials too. They might have been some allies of the Avars proper of some kind, probably. One of them is about half Avar (1/4 East Asian, 1/4 Caucasian) and half of this clan. So his father likely married an elite bride from the East to confirm the alliance or something like that.
While FTDNA hasn't analysed the Avar samples yet, TheYtree does provide us with some kind of preliminary results which are highly interesting.
First off, there is indeed one big CTS9320 clan it seems, and all downstream assigned individuals are:
E-BY4518 -> E-TY507088
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This haplogroup is widespread in moderns, among others Austrians, Hungarians, Slovaks, Poles etc. At first look it looks distinctly Vekerzug-associated and possibly spread with both Celts and Romans, plus apparently Avars.
Other downstream assigned branches are:
E-FT356146 =
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Very rare, among others German and Armenians, could be Vekerzug/Sarmatian associated as well.
A larger group of samples might be assigned to:
E-L241 -> E-BY5682
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Unfortunately, only one could be assigned that far, the others are either stuck at S2979 or L241, but this is likely a second clan group of Csokorgasse at first glance. The distribution is fairly wide, similar to E-TY507088.
Since there was yet another branch identified before, we deal with 4 lineages in total, of which two seem to have multiple members. A lot of the samples couldn't be assigned downstream by them, we'll see what FTDNA can achieve with the data set.
The general distribution of these haplogroups looks to me, at first glance, rather Central European centered.