Cheerwine is probably as old as Moxie. It's been around a long time, and, in many areas, was the soft drink of choice, perhaps along with Sundrop.

Blenheim is fairly recent in popularity, even regionally, I think, but makes a pretty good ginger ale, as long as you like it in one of their flavors, hot or hotter, and you don't require any ginger to be in it. (Though I just discovered that it's now owned by the folks who own South of the Border, a tourist trap that North Carolinians are glad is in South Carolina, even if just barely, and that might be reason enough not to buy any.)
I'm not familiar with Red Rock, though. But you can't forget about RC Cola, also a southern beverage specialty. And don't forget that both Coca-Cola and Pepsi were invented in the South. Most fo this stuff is in the Georgia/South Carolina area. Apparently, southerners like their sweet beverages (don't forget about iced tea, which is much different south of Richmond than you might expect, and, in many cases, as sweet or sweeter than your average soda).