DC/DC converter in parallel with analog circuit
The important detail is "It's an EMCO Q15-12"

This is a 1.5kV output with DC control and operates from 12V

IT is rated for 1.25W and so you should operate from 12Vdc and use a pot to control the output voltage via the control input as shown in the datasheet.
datasheet

If this is an option you don't have use a 1W LDO such as a LM317 to control the voltage with a suitable pot and fixed resistors to control the Input voltage from 2-10V to get 0.2-1 kV out. 

To speed up the decay time you may consider applying a 1W resistor rated for 2kV or 4x500V equal 1/4W resistors in the range of 250k to 1 M

your voltage source impedance must be &lt; 1% for 1% load regulation.
If 1.2W at 12V input average impedance is 120 Ohms so your regulator impedance needs to be ~1 Ohm

If you are only consuming 0.1W then the source impedance can be 10 Ohms.
A voltage regulator with 500mA drive capacity at 12V and drops only 0.1 V has an ESR of 0.1A/0.5A or 200 mOhm for example and easily satisfies the load regulation you desire.

The real impedance of the converter on surge startup depends on its primary winding DCR so startup current can drop your high impedance source below its required startup voltage of 0.7V ( Vbe ) which is why your circuit failed.