If you have a look on Window1 theres a way to create Childs via FigureShapes and CurveShapes. How to make this working with DrawSunburstChild? Maybe someone will have fun to check my conversion and fix it.
Actually, there are other differences. In particular, the sunburst chart can also have more than two segments in an outer ring for a given segment in an inner ring, and the sizes are possibly proportional to other quantities instead of strictly equal. But it should be possible–though not necessarily trivial–to rework the fan chart code for a sunburst.