i guess the core is saturating on resonance is not working like a normal transformer... its a ringing transformer...
the saturation may be at the top limit voltage along with corona discharges when the coils are not in oil...
i got up to 50kv in oil no proble.. but in that case there was two cores one with primary and secondary and the other with the chokes....
yes kitchen oil

i notice the saturation in the primary when it start to decrease primary impedance.. i have a meter for that so basically the resonance is the top limit... is it that saturates the core.... should not be bad... but the more coils the lower energy dissipated on the core and probably higher voltage... but also slower