Its not a question of re-doing the pcb but getting a good Strong waveform. It is clearly seen that the GDT is absorbing a lot of power and exhausting the available power from the drive. The waveform clearly shows this and charging the gates is taking forever, hence the slow rise and fall times. Your best option I guess is to make another totem pole after the drive to add some current to the primary of the GDT. If you like to try something else well considering the GDT primary inductance is only 500uH then you can put a 10 to 20 ohm resistor in series with the primary to limit current. (remove everything else and feed from the drive directly) This may cure the problem. Do not forget that with a 2 switch converter you are driving 2 gates simultaneously. Experimenting with the resistor value may get you a good balance to get enough current and not loading the driver chip more than necessary.