Another thing to remember about these “double-barrel” Senate races: the last time two parties split a pair of such races was 1966 in South Carolina. In this case, given how the two candidates of both parties often campaigned together as tag-teams, I still think it would have been highly likely that the same party wins both races.
One of the two in that double-barrel was of course Thurmond, who had a very strong personal brand that overrode the still-nascent realignment of the state at that time. I think that a split result in the Georgia runoffs would've been more likely than in many double-barrel races due to the clear differences in coalitions between the two (especially Perdue's overperformance in GA-06), but it was still always unlikely that there would be a split.