some similar designs
What I saw in Gori and Uplistsikhe weren't Armenian khachkars - just local stone tombstones with carved decorations. This tradition could form only in areas where soft stone available - in Uplistsikhe they carved a city out of this stone exactly for this reason.
Greater Armenia existed 1500 years ago, and, it looks, even at its best time didn't include the Gori/Uplistsikhe area.
There are khachkars in Georgia near the Georgia-Armenia border, Javakheti region.
I just found what the ruins (with the tombstones) I visited - old Uplistsikhe village abandoned in the XX century. People were re-settled to new Uplistsikhe, no Armenians live there.
The place in the 1970s. The source
The 1900s. The source