Could you use these ones instead the reference you used?
Southern is Armenia Medieval, and Northern are 2 Russian Caucasus Medieval references (One close to Abazins&Karachays&Circassians and the other not very close but tending to Darginians).
Code:
Southern_Caucasus_Medieval,0.105476,0.133034,-0.054054,-0.050065,-0.030159,-0.0073443,-0.0005483,-0.0070767,-0.0310873,-0.0059533,0.001949,0.0017987,-0.0071353,0.000413,0.0021263,-0.0034917,-0.0018253,0.002914,0.0038967,-0.0005837,0.0016637,-0.000371,-0.0008217,0.000281,0.0034723
NorthernWestern_Caucasus_Medieval,0.1188314,0.0903822,0.0257952,0.0970292,-0.0369914,0.0405508,0.0111864,-0.0031846,-0.0591484,-0.0712908,0.000942,-0.0014986,-0.0027056,-0.0181112,0.0364272,0.0144256,0.009909,0.001064,-2.00E-07,0.0071284,-0.0035938,0.0059848,0.0126454,0.0164842,-0.0050294
NorthEastern_Caucasus_Medieval,0.1104083,0.0832733,-0.0214957,-0.0169037,-0.0338523,-0.000186,0.0067367,-0.002769,-0.0509947,-0.0165837,-0.003302,0.0073937,-0.014222,0.0031193,-0.0009953,-0.005392,0.0209483,-0.0035473,-0.00595,0.0081707,0.0027033,-0.0018547,-0.0032457,-0.003173,0.002395