Joystick Emulation
What do you think of the idea to handle the mouse like a joystick: D2X-XL measures how far the (invisible) mouse pointer has been moved out of the screen center, and moves the ship to the same direction. Distance from screen center determines movement speed (up to the built-in limits - mouselook will not be active in this mode). Ship movement will cease when the mouse is brought back into the screen center (or to be precise, into a small deadzone around it).
I tried it and found that you could get the hang of this pretty quickly. I also found that not having a physical center position like with a joystick didn't pose a big problem.