Well, in fact most of the villages of Tur Abdin are organized by clans but the problem is now, nobody use it.
Midyad : there are big families who took control of the town : Saido, Challma, Bisse... Some people of these were really influent and were considered as "agha" (sorry for this kurdish name) like Abdo Zette who has his own men, at that time, syriacs were respected, for the best and for the worse, even by kurdish "agha".
Iwardo : same things, there are 12 clans.
Mzizah : the syriacs of Mzizah are from Iwardo, Masud was a great man of the village and still during the genocide when he was the leader in Iwardo. He ordered his men to go to each village under attack to save them and to take them to Iwardo. He was the one who organized the resistance.
Sare : as you said there is the family of the great Chamoun Hanna Haydo, kurdish "agha" considered him like their equal. His goal was to create a tribal system in Tur Abdin, He wanted to unify all the clans, for this he went to Arbo to talk about this with 2 prominent families Beth Arsan and other one which I have forgotten the name...One of these families rejected the idea...maybe if not, our destiny wouldn't be the same.
Kfarze : there are 7 clans (bavekat), the name of one is khuwaja (where I'm from), other people call them the family of aghas, I think there is a link with the signification of khwaja because if you take a look at wikipedia, it's a noble title used in middle east, central and south asia. I did a little research and I haven' saw another one christian family named khwaja... A brave named was from this family, his name was Abdo. After the genocide, he broke the mosque of the village, he urinated where muslims wash theirs hands and others, and he cleared off them from the village. For years they didn't show up and they did just after the murder of Abdo.
I don't have other information concerning the other villages
Sorry for my english! I'm not really fluent...