John, do you know about localized steam bending? Marc St. Louis featured this technique in one of his PA magazine articles. You basically wet a piece of cloth and wrap it around the wavy spot you want to make flat then wrap foil tightly around the cloth. Heat the area with a heat gun while the wavy area is under pressure with clamps. Heat for a couple minutes and the water turns to steam and the area should be pliable enough to take most of the wave out (don't heat longer than 5 minutes).
You would want to do this at floor tiller stage when the wood is thin enough to bend.
I tried it on an elm stave a year or so ago, and it got most of it out.