Planing concave surfaces used to be significant problem in the old days of wooden boat building. They did it a lot when shaping the back of the planks on a carvel planked boat. The old time boatbuilders made all their own planes and typically used a wide variety. They carved them out of solid blocks of wood. The only metal in them was the plane iron its self. A good reference on this topic is "Building Classic Small Craft" by John Gardner. He has a whole chapter about boatbuilder's planes, including "backing-out" planes for shaping the concave backs of the planks. Sounds like a good winter project to me.