"(a) Georgia-the-state is significantly older than Georgia-the-country,"
I'm awestruck. Awestruck.
Technically speaking, modern Georgia has only existed since the fall of the Soviet Union (or there abouts), which is presumably what Matt was referring to. The article does, however, include plenty of information about pre-Soviet Georgia, so that argument doesn't really hold water. Were the article specifically about modern Georgia, he would have a point.
The state is bigger in terms of population and economy, although (according to Wikipedia) it is slightly smaller in terms of area, which I would consider a "measure [I] care to name".
I really don't think there is a better solution than to have a disambig page. There are two major meanings to the word, so we list them and let the reader choose. It works.