Using Gan Fets as a signal switch

I am attempting to replace part or all of this signal switch with just one gan fet, the input is connected to a coil driven with -15 volts pulses and flyback is clamped at 200 volts, the first mosfet gate is driven with + and - 15 volts and works fine, i modified the drive to use a gan fet 5+ and 0 ground, but no mater what i try the gan goes partial short gate to source, Not knowing too much about gan fets is there a way to make this work?