OK, looking at the output in more details, I've realised the parallel cap is way too low. Increasing its value to 3.2uF, then decreaing R1 to 9000 ohms and increasing R2 to 500 Ohms results in much nicer results. Decreasing the output cap to 100 uF results in a fairly rough approximation of a sine wave, and the program tells me the power across the resistor peaks at 0.16W.
Now to go out and buy some more capacitors. My largest on hand is only 10uF.