Transformer for electrostatic speaker (high voltage, very low current)
So the question is whether there is another way to get high DC voltage
  when I can't get my hands on an up-to-spec transformer.


There is no option, you need to pass high voltage audio to the plates and this can only done using a transformer: -



The picture above shows your power amp (to the right) feeding the LV side of a step up transformer. The turns ratio is \$\sqrt{\dfrac{20k}{8}}\$ = 50:1 stepping up.

The DC bias supply feeds the centre tap of the HV secondary and to create that bias supply requires one of these: -



or maybe even one of these: -



Cutting thru and getting to the point, if you did not realize that you are likely to electrocute yourself - yes I know that's a generalism but this thing can kill you.