Is Georgia (the country) even possible to crack in tracing genealogy?

Hello. I’m struggling with a significant piece of family history, as there were some births and a marriage in Georgia (the country) that are seemingly impossible to trace. This region is also part of my DNA.

Through records from another region, I’ve managed to find some names, a parish, a town and some approximate years, but none of this has helped as digital records from the region don’t really exist on the usual sites.
The parish no longer seems to exist either and my understanding is that those who have tried to reach out to parishes or record offices in Georgia directly haven’t had luck in getting replies, which makes sense.

The initial records I’d be looking for would date from 1890s through to about 1910-15 or so. Russian Empire times, further complicating things.

Would anyone have any suggestions for resources I may not have thought of yet? I haven’t wanted to accept this roadblock as permanent, but realize I may have to.