After splitting the billet and then joining the pieces, the 'inside' has to be smoothed. I use a variety of planes, starting with an old Stanley scrub plane, sometimes using a small block plane, and finishing with a long jointer, mostly across the surfaces, side to side, with increasing thin shavings being taken.
Flattening is somewhat annoying -- most of it will disappear. When it's flat, lay the rib assembly on it, and trace it. This little bit near the tracing will remain. That outside of it will be cut away. And just inside, it will be scooped out after the outside is finished.
Figured maple is tough wood to work. Here is the same piece, flipped over, with a rough outline and the start of the arching.