I can't speak for the US since I don't live there although I admit it is a very big market...

In wine producing countries in general, and the US is one, one will encounter a lot of 'non tariff barriers to trade' (i.e., administrative challenges) that make the import of foreign wines difficult. To be frank, and despite the expense that you correctly underline, I can only imagine doing so with the help of an enthusiastic importer.

I know a retailer in Switzerland who would probably love to import Georgian wines (and many others, as long as they fit his taste) but the quantities would be so small to not even be worth your time.

Anyway, I do hope to visit Georgia one day and your cave.