I just found some advice on these forums suggesting to set the series holeSize to zero. When I do that, the inside donut indeed becomes filled in, but the gradient colors still show the chart as a "donut" with a lighter ring of shading in the middle of the chart.
If that is the only way, I can live with the weird gradient, but how do you make one chart thicker than the other? After setting the holeSize = 0, the outer ring got thicker to match the inner "ring" (i.e. circle).