I reel with the hand that's upcurrent. That way I set the hook with the rod instead of the reel handle. Saves on equipment malfunctions. I've broken a reel handle or two by yanking on it instead of the rod handle. Switching sides takes a minute or two to get used to, but in the end it's been the best way for me to maximize my hookset to catch ratio.
This is a real (reel???) problem with paddlefishing. Reel handles take a ton of abuse from people fishing the left side of the river. For those that don't already know, the "left" side of the river is determined by looking downstream.