Help needed for HV DC/DC converter
Your diodes and transistors are insufficiently rated for the voltages you need to block in this inverter. So, frankly, you need to beef up this thing significantly if you want to do 100V. Hell, that's 20 V above the maximum ratings for the BD139 – an absolutely wrong and obsolete choice!

Anyways, this system is really not what you want for a 100 V source: 


unregulated/uncompensated: The voltage generated by the Joule thief was not a design target; it was just supposed to be "high enough". You're building a measurement device, so you want to know what your voltage looks like. You need a closed-loop control mechanism that takes temperature drift and component tolerances into consideration
low-speed switching: It's hard for me to estimate what this will oscillate at, if at all, lacking any information about the transformer. But: I doubt it'll be a high frequency. You said you want a small inductor, so you want high frequency. Replace the  self-oscillation by something that forces the thing to work at a specific switching speed range.
Safety: well, nothing here is isolated, you're not fusing your output, so, if this can reliably deliver >20 mA, it is dangerous.
Transformer windings: you're not specifying, but this looks like a 1:1 transformer. That's kinda bad if you want to make large voltage jumps: a higher winding ratio would help you increase the voltage in itself! 


Especially the last point highlights that this is not the switcher architecture you're looking for.

You probably want a flyback-based DC/DC converter.  I'd recommend you go for something simple and robust, like good old TI LM25xx regulators.

In fact, I just went to ti.com and clicked through to the design tools and the power designer, said I had an input voltage of 10 V – 13 V and wanted 100 V at a max. current of 0.02 A, and was greeted with this:



This circuit has specified ripple, it's way more efficient that your circuit, and, considering you safe a lot of transformer cost by having a smaller one running at a higher frequency, probably even cheaper than your hand-tinkered one. 

however, this was the design I've got recommended when I went for "minimum BOM count"; when you go for "minimum BOM cost", you might get something different, as you'll get something different when you go for "maximum efficiency" or "minimum space".