Got it to work...instead of both graphics (polygon and point) originally referencing featureSet.features[0];, I created a new graphic for the polygon (which didn't need attributes). I also added these to one graphics layer. Working code is below:
var graphic1:Graphic = featureSet.features[0];
var polygon: Polygon;
var centerPt: MapPoint;
polygon = graphic1.geometry as Polygon;
centerPt = polygon.extent.center;
graphic1.geometry=centerPt;
graphic1.symbol=myInfoSymbol;
var graphic2:Graphic=new Graphic(polygon,myFillSymbol);
graphicsLayer.add(graphic2);
graphicsLayer.add(graphic1);