Am I a liberal Republican or a conservative Democrat?

[Never]

Let's take a minute to remember that not even Thad Cochran and Eric Cantor are conservative enough for today's GOP.

I think that answers your question.

That doesn't really explain the entire picture here; abortion supporter Gov. Brian Sandoval is accepted by the GOP...

Anyhow, I think that OP would do fine in either party. He could be a John Barrow Democrat, but it's worth noting that the Blue Dogs like him are becoming a smaller segment of the Democratic party. Down in Georgia, Nathan Deal was a founding member of the Blue Dog Coalition, and now he is the Republican governor.

[Never]

Let's take a minute to remember that not even Thad Cochran and Eric Cantor are conservative enough for today's GOP.

I think that answers your question.

That doesn't really explain the entire picture here; abortion supporter Gov. Brian Sandoval is accepted by the GOP...

To be fair, Sandoval represents a state that went for Obama twice. Even the most extreme Tea party activists at are more likely to tolerate a republican moderating in a Democratic state than in a Republican state like Georgia.

Very true, but it is important to understand that neither Republicans nor Democrats are monolithic across the nation, as you pointed out.

Yes, Georgia is a conservative state with conservative senators, but some other Southern Republican states have relatively moderate senators (like Lamar Alexander in Tennessee and Lindsey Graham in South Carolina).

OP does have some fairly moderate views, like support of immigration reform and belief in global warming, but there are Republicans in the South who support both. Mike Huckabee believes in global warming and as recently as 2008 argued that we should do something about it, and Lindsey Graham believes that there should be immigration reform (so does Marco Rubio, though I don't consider Florida to be a culturally Southern state like Georgia, and of course, Florida is a swing state and Georgia is a Republican state).