perhaps their sacred polyphonic music and the Notre-Dame School organa have a common but lost Byzantine root?
Something of the kind seems very likely, doesn't it?
Of course, Georgia wasn't always cut-off in obscurity - during the times of David The Builder, and King Tamara* prior to the Mongolian conquest in the Middle Ages, the Georgian court was an active, if distant, member of the European circle of royal families... Princesses from "Trebizond" married into the Hungarian and Bohemian royal dynasties. Maybe this intercultural activity in the Middle Ages extended to music too?
*
she had to be called "King", because medieval Georgian had no word for ""Queen" (For anyone who missed it, the prog is available on Listen Again, and Part Two is broadcast on Sat Dec 22 at 15:00 London Time)