I am designing a H-Bridge based DC-DC Converter that boosts 24V to 350V DC. I use a HF transformer at the output of the H-Bridge for the actual boost. The circuit works OK for a while and then the IC dies. I suspect this is because I have ringing present at the output of the H-Bridge. The first picture below shows the output without the transformer and the second one shows how the ringing increases with the transformer.
My layout currently is on a single layer board and I will move to a 2-layer board to minimize loop areas of signals that drive the gates of the MOSFETS - but wouldn't the inductance of the transformer always cause some ringing? If so, how can I be sure that it won't damage my chip? The half-bridge driver that I'm using is MAX15019 and it can tolerate -5V to 130V at the output pin so I'm mostly concerned about the negative transients.
The following schematic shows the circuit. The graphs are measured at nodes A and B with respect to GND (this is also where the transformer's primary is connected). Note that I have tried various values for the gate resistors and using a higher one usually just leads to more power loss in the transistors. As mentioned before, I am concerned with minimizing negative transients - particularly when the transformer is connected.