Gas ionization is a good source of broadband noise, even with a large series resistor the distributed capacitance will charge up to the ionization voltage and very quickly discharge into the tube. This will produce a very quick and sharp current peak/spike rich in spectral content.
Edit: Instead of a neon bulb why not use an LED (maybe multiple LEDs) on one, or more of the DC outputs, just use the series bleed resistor(s) already in place.
Why such large capacitance on the transformer secondaries? This isn't necessary and even increases power losses and these large capacitors have a large effective inductance which hinders their ability to provide a low impedance shunt at higher frequencies where they help reduce noise feedthru.
BTW, those custom toroidal transformers look nice!!
Best,