What you need to do is put a scope on the output of the FEZ when it’s rebooted, work out what’s the voltage of an undefined pin upon reboot. Now what you have is a potential divider, where some of the voltage is dissipated across a pulldown resistor, and the rest across base emitter junction of the transistor.
What you now need to work out is the maximum voltage you can affoard across the transistor without triggering the circuit, and work out the two resistor values (keep in mind on resistance of the transistor and resistor value tolerance), for the base and the pulldown.
What you want is for the voltage on reboot to be below the threshold that triggers the circuit, and the voltage on pin high to be above.
Another thing you could do is just slap a PNP transistor from the pin to ground, that is connected to a “Ready” pin, that turns on when the chip finished initialising. That would pull all those pins down hard on reboot.