Originally Posted by
yankeefan
Its especially problematic when I'm out of the saddle and rocking my bike
Then don't rock your bike. Learn how to stand and pedal without throwing the bike all around.
You want fun? Try two panniers loaded with groceries (about 30 pounds each) and standing. If you rock the bike then, the pendulum effect can knock the thing right off its wheels.
In other words, the single pannier isn't the problem. IME.