I think you're mistaken.
As far as I know, the leading Oriental Orthodox Church in Georgia is Georgian, and is now headed by His Holiness and Beatitude, Illia II Archbishop of Mtskheta-Tbilisi and Catholicos-Patriarch of All Georgia, and they are not from the syriac tradition (syrians), they are more closely related to the Byzantine Empire, at the time Oriental Orthodoxy gained the good favour of the Emperor.
Patriarch Ilia is definitely Eastern Orthodox.
The Georgian Church initially rejected Chalcedon during the 500's. However, in the early 600's they accepted Chalcedon. Ever since then, they have been Chalcedonian.
I've already posted on Georgia's autocephaly from the sources:
Interesting bit on the autocephaly of Georgia:
And they came to the borders of Armenia and Byzantine lands... http://rbedrosian.com/gc5.htm
Note: the granting of the 12 bishops was to make the Catholicos fully ennabled to act as an autocephalos Church.
C. Peter ruled (467-474)
Imperial policy did not swing to the non-Chalcedonians until the Henotikon of 482. Gennadios I succeeded St. Anatolius (who presided over Chalcedon) as EP in 458 (to 471): he had opposed St. Cyril, his works latter quoted as being worse than the letter of Ibas. He reconciled with St. Cyril at Ephesus.
The Emperor exiled the non-Chalcedonian successor of Dioscoros when the Chalcedonian successor was murdered, in 460, on the advice of Gennadios, on the word of Pope Leo (who wrote the famous Tome at Chalcedon). Exiled to Sevastopol, Crimea, towards Georgia.
The Georgian royal family did marry into the Imperial family (the Helen in the linked post), all of whom were Chalcedonians.
The Patriarch of Antioch who made Georgia autocephalous was non-Chalcedonian, Peter (the Fuller).