Unfortunately the current flow is essential, because the source of desired "overvoltage" is the inductive energy storage (1/2L*I^2).
I don't disagree, but this is a 200H+ coil which will operate with 2kV on one terminal and 8kV pk-pk on the other terminal.
Not something you fling together on a rainy Sunday afternoon. The QUAD transformers are build for this.
Jan
Unfortunately, the choke must be design for constant idle current which is must be equal or greater than the peak value of current of worst case scenario. Must be implement a necessary wire gauge, which is a lot of bigger, than the transformer's secondary which intended at same peak current (see music crest factor). The thick wire needs bigger bobbin and core. These factors cause higher coil capacitance which must be handle (thicker insulator layers and winding's tricks).
Jan- why do you not want to take advantage of the transformer to its full utility? See below- Tie the center tap of the transformer to ground. Two tubes in push pull tied to the negative supply (no positive supply needed). The transformer DC is balanced out so no saturation issues as long as everything is working. You can operate in class A or class AB by tweaking the bias. You could cross couple (cf MacIntosh) with the transformer secondary tied to the cathodes. Feedback from the plates via caps is a precaution that may not be needed. The drive circuit could be two opamps depending on the tube requirements. Keeping the plates at ground should be a significant safety issue. Add some series air core coils to the transformer to extend the response.