My first idea for forming a horizontal base was to use these wedge-shaped pieces.  If I had a bandsaw, I would have cut the wedge out of a single piece of wood, but since I didn't, I cut multiple wedges using a jigsaw and glued them all together.  The problem I had was that I couldn't cut the wedges very uniformly and once glued together, it was difficult to shape the wedge to match the bottom of the cradle.