I don't think it would be that much of a problem, especially if you will have access to internet weather reports daily. With 10-day forecasts, you can get a window large enough to cross the south. From there, you may need to wait out storms or re-route. It is probably a week's worth of riding, so if you can set aside 2 weeks it should allow plenty of time to go around storms. Worst case scenario; you can rent a small u-haul to finish the trip. You may as well see some sights along the way too.