First-off, Descent should work just fine with the twist axis of a joystick; even the original retail game never had any trouble with me assigning it to bank. It should have no problem recognizing HAT switch directions, either. I don't think my old crappy Wingman Force 3D gave me any trouble, and that wasn't that far off from the Extreme. Does the controller config in the Windows control panel detect all of your joystick functions?
Secondly, I go with an all-joystick setup myself, though most people in the community seem to prefer either joystick+keyboard or mouse+keyboard. My joystick's X, Y, and Z axes are assigned to yaw, pitch, and roll, respectively, and I use the throttle for acceleration/deceleration. The HAT switch handles sliding, a button on the base of the stick controls the afterburner, and the primary and secondary fire are controlled by the trigger and main secondary button. There are quite a few joystick people who dump lateral motion and sliding off on the keyboard. Sushi's post contains a feasible mouse+keyboard combination, but there might be a few movements in there that are somewhat awkward to pull off. The most important thing to remember about Descent is that your config needs to allow you to move along all six degrees of freedom at once, while also firing weapons and working your afterburner. It's a bit of a tall order, but if you tweak your config enough, you should be able to find something effective that works for you.