Hey Albert,
That's great news about your modulator. Good luck with the build.
I'm not quite sure where your break out is happening, can you send a pic? If it's some way down the secondary, that's often a tuning issue. But yep, pic will help.
I don't quite understand what you mean by 'Bach on square wave.' Can you clarif - I love Bach but this is an alien concept and sounds like it would have all sorts of harmonic impurities.
(I know that we can square up a signal with a Hex inverter chip with Schmitt trigger, like 74HC14 - this is often done with digital Tesla coils and current feedback. So it's not I don't know how to do it, rather I don't know why in this case.)