How do I improve and isolate from mains ground my Tesla coil control circuit?
I would eliminate the feedback loop from the transformer secondary (HV) and use a simple oscillator  (e.g. 555) to drive the '151 FET driver. Then you can fully take advantage of the isolation provided by T3.

I would also consider adding a snubbing diode across the primary of the tranformer to knock down the transients into the supply.