If the potential difference of the primary terminals is 30kV the coil will instantly be destroyed. It is basically a short circuit with some inductance.
I am not implying the 30kV voltage is across the primary, you have to create a way to generate the correct voltage across the primary that is _not_ referenced to chassis ground and that return needs to be floated to 30kV. I don't think that a coil can take that as the case would also be floating at 30kV and all sorts of arc points need to be addressed (internal to the coil between the windings and the case as well).
If a coil was a 4 terminal device with separate ground terminals for the primary and secondary AND there was enough standoff between primary and secondary to withstand 60kV/90kV then the primary driver could be referenced to chassis ground on all the coils and driving the primary would be much simpler.
