First thing that comes to my mind reading this is the Chattooga river (I go fishing there alot), which would most definitely be a suicide mission at flood stage. Even the shallow areas that used to be fords for the logging roads would be deadly at that point.

Even so, some sort of flotation is the only way. If possible, throw something attached to a rope to the other side and see if you can snag something. If so, and you hang on to that rope, the current will swing you to the other side rather quickly without you having to do any paddling.