High voltage Dickson charge pump switching
You already have nice high-frequency (2.2MHz) AC at the converter chip SW terminal.
Try adding 2 or 3 more stages to the converter and 2 stages to the feedback divider. Each converter stage is 2 diodes, one resistor and 2 capacitors. Each feedback stage is 35.7K in parallel with 150nF.

Obviously you'll have to increase the voltage rating on C7 as well.