In this circuit the D2 and R3 with their resistors do absolutely nothing, because they are plain parallel to the diodes within the bridge rectifier (and that is connected without any resistance at all, so will take all current in that direction).
The capacitors directly connected like this mean there is 0.5uF directly parallel to the lamp - that is quite too high to cause problems with current spikes like
with capacitor only ballast. It does not matter that much, if the capacitor is in series with a low impedance voltage source, or parallel to the lamp. In both cases the lamp sees the capacitor as the impedance and that alone causes those current spikes.
So better connect the resistors in series with each of the capacitors. It will be still sufficient in the doubler mode for ignition, because there is no current (so no voltage drop), but once the lamp ignites, these resistors will separate the capacitors from the discharge.