I have yet to attend a Georgian Church to find out the answer.
I only mean that most of the nearest churches next to me don't follow sing the prokeimenon or alleluia with the traditional (sometimes more difficult) byz. melody or variety that they are ment to.
I do believe that the Greek Cathedral in Washington, DC and one in Lancaster, PA do use Karas Alleluias (which would be enough).
The full Prokeimenon melody seems to be something impossible to find though.
I haven't yet fully explored all the options of different churches. I live in an area where, within a one hours drive is a wide range of choices for Orthodox Churches. I do have options of two Georgian Churches and one Georgian Monastery, about 7 greek ones and too many others to name.
In time I will find what I am looking for as regards Byzantine rite parishes, but as I am with a Western rite mission, it's not really my concern to do too much Church exploration/hopping. For me the byzantine rite parishes are moonlighting, and WR is full time.
I can say that the St John Chrysostom Antiochian Church in York, PA has one of the best choirs I've yet found. People who enter that church really do experience heaven on earth! http://www.youtube.com/watch?v=avRz7FqbGZ0&feature=plcp
They have several videos online, but they dont quite compare to visiting it in person, where in my experience you hear even higher caliber of sound and challenging pieces than that heard in some of their older videos.