The TVA was created back during the Great Depression, so how come it took so long for this area to swing to the Republicans? Western Tennessee use to be Democrat back when they were Dixiecrats and many of the Southern Democrats favoured segregation, but today it is quite racially polarized like much of the Deep South. Eastern Tennessee was always Republican, even during the Reconstruction era. But Middle Tennessee until very recently tended to favour the Democrats. Even Kerry won several rural counties in Middle Tennessee.
Well, Gore was also from central Tennessee. That definitely helped in 1992-2000.
But you sort of answered your own question: There were specific reasons for western Tennessee to abandon the Democrats and embrace the Republicans (civil rights), while such reasons did not exist in central Tennessee, where racial tensions were weaker and Dixiecrat politics mostly nonexistent. Central Tennessee switched to the Republicans on social issues, but not on race. Rather, it found the charismatic religious appeal of the Republicans far stronger than decaying TVA ties to the Democrats. Plus, around the 1990s those who actually remembered the heyday of the TVA started dying.
It is also worth pointing out that even Obama won two rural counties in Central Tennessee (Jackson and Houston), both old TVA counties. The TVA counties stick out like a sore thumb on the 1988 Presidential map. Also, see the 1964 Presidential map to demonstrate the strength of Dixiecrat politics in western Tennessee against its weakness in central Tennessee. Wallace did do well in central Tennessee, though; not sure why.