A d-pad (digital interface) will usually hold the input high, and will not see that input as being activated until the voltage drops below a certain threshold, based on the interface in question.
What you would need to do is increase or decrease the amount of resistance between the ground on the joystick pots and the interface you are using, to get the adustability you desire. I.e. more resistance=larger deadzone, and less resistance=smaller deadzone. Resistors in parallel reduce resistance, while those in serial increase it.
That's the theory. In practice, however, it may not be simple to do, and would likely entail quite a bit of trial and error.