I'll intercept, I think yes but, and I do know it's a longer drive, I think you'd probably be in even better shape driving further and going into North Georgia. I think you're probably not far from I-59 if I remember your location correctly as you have had it before, if it were me, I'd simply get on I-59 and drive into Northwest GA, then get off I-59 and head east some. Not exactly sure where I'd stop, but one guess would be maybe Blue Ridge, GA (to not take it too far). If you were to choose to do this, lol, any more that you can get will need to be looked at in a map. I know Northwest GA fairly well, but not sooooo well I can give a lot.
If that's too far, while I do think all of far North AL might see snow, I still think far NE AL is probably your best bet. That would be the same thing of find I-59 and just drive until you don't feel like it anymore (with that hopefully landing you in NE AL). Although that does include a small issue, NE AL is pretty to me when I've been there, but there's almost nothing there until you get to the Chattanooga metro, if you were to need some accommodations.
Edit: Just looked at the NAM, if that case were to be true, that firms up what I think. Areas west of the Carolinas that are in the best shape might include far NE AL.