The oscilloscope waveform shows Vds near maximum rating, likely to damage the transistors by continuous avalanche breakdown. Drain to gate short will then burn the driver IC. Although there may be additonal problems (and even other first failure causes) you need to sort out the overvoltage problem, e.g. by adding RCD snubbers or fast diode+zener clamp circuits to the drain nodes. Achieve operation at 30 to maximal 40 V Vds,peak and see if the problem disappears.
Reducing transformer leakage inductance might help, but a snubber is probably still necessary.