CF is very stiff. If your pedal stroke is prone to mashing (pushing down all the time) instead of a smooth, round, circular motion, this would probably explain the "wobbling." Think of every time you push down on the pedal, you're putting all of your force on that side of the bike... that will definitely make it "wobble" from side to side. Try focusing on a smooth pedal stroke going in circles and see how it feels. The fact that you don't notice this while coasting makes me think more so that it's in the stroke.

It's always in the stroke.