Is my power supply calculation correct?
Typically when spec'd at x V AC, this is RMS (assumed to be a sine wave).

So your V AC calculations are more or less right (9V AC in the middle, 171V AC at the output), but you need to multiply the rectified values by \$\sqrt{2}\$ to get the peak voltage and subtract off 2 diode drops for a typically 4 diode bridge rectifier.

Assuming you're using typical silicon diodes with \$V_D \approx 0.7V\$, the 9V AC becomes 11.3V peak and the 171V AC becomes 240.4V peak.

Also, you'll probably want some decent sized capacitors otherwise you'll end up with rectified waveforms which look like \$abs(sin(t))\$: