But if that is just being used to drive a FET you can swap the transistors so the NPN is on top and the PNP is on the bottom. Then you won't need to worry shoot-through since they will use each other as negative feedback so both be fully on at the same time.
There must be 100 Gate Drivers for MOSFETs like this. This one will allow the top and bottom transistors to be on at the same time but some have a function to stop two transistors on. Some have a delay for turn-on/ turn-off. Many options. This one is good for 600 volts.
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