DerStrom8
Super Moderator
To get variable current and voltage he is going to have to use a inverter drive of some sort and to get to 20 KV at 1200 watts continuous duty this thing is most likely going to need a custom wound transformer regardless of what frequency it's running at and none of this is going to be overly small or cheap.
As far as variable voltage and current goes with NST's that's easy. Just use two variacs. One is the voltage control and the other is wired in series with the NTC transformers primaries to work as a variable inductance type current limiter.
Standard old school Tesla coil driver circuit tech.
The problem with using NSTs and Variacs is that they're very large and heavy. Again, the host would like the setup to be as small and lightweight as possible. Otherwise, I'm sure he would have already used the setup you describe.