Another viewpoint: TVS diodes are not particularly fast but simply rugged large chip zener diodes. The junction capacitance can be expected respectively high. Thus my suggestion is, you can use TVS diodes if you have no problems to drive the extra capacitance. It's no problem with medium speed multi kW IGBTs, but possibly unwanted with smaller and faster devices.
It's not clear to me by the way, why you are trying to drive the gate voltage up to the limits.