Shea--I can probably tell you more about Georgian music (from the Caucasus, not the Southern U.S., though I know a bit about that kind of Georgian music, too) than you want to know.
Let's start with a few websites, each of which has some audio samples you can listen to, and sometimes lyrics, often transliterated in the Roman alphabet:
The Kartuli Ensemble, which I co-founded back in 1983, currently based in the Hudson River Valley of New York Iveria, the Boston, Massachusetts area branch of the Kartuli Ensemble.
Darbazi, based in Toronto, Canada, founded by Alan Gasser.
Mariani, based in Paris, France. Some of this website is in French, but the group was founded by Frank Kane, who was the other co-founder of the Kartuli Ensemble, and is an American by birth (though he's become a French citizen).
The Kavkasia Trio, who are three members of the Kartuli Ensemble who have taken the time out of their lives to go professional/semi-pro: Carl Linich (who taught at Village Harmony and is bringing Georgian music to Vermont, and who lives half the year in Tbilisi with his wife and child, where he participates in professional Georgian singing ensembles), Alan Gasser (of Darbazi, and Toronto, Canada [see above]), and Stuart Gelzer, who lives these days in Fredericksburg, VA, where his wife teaches at Mary Washington College. (N.B., this web site isn't good for much more than ordering their album.)
The Rustavi Choir/Chorus is Georgia's finest ensemble, and has been for many decades. This is not an official webpage, but has music samples for the listening in MPEG format.
I haven't put down a discography here (though there are now many CDs available, including folk, classical and liturgical). If you're after lyrics or sheet music, I can help, but my collection has hundreds of items and I'm not about to post it here. (Some of it is untransliterated in the Georgian alphabet, but I can transliterate it for you if you need that.)
If these web sites don't answer your questions, pst a specific question, or send me a personal message and I'll get back to you via e-mail, snail mail, or telephone. I've got a couple of decades of experience and involvement since I first asked the questions you did (in a pre-internet, Soviet-era time), and I'd be happy to share.
--Charlie Baum