From my perspective, if I could simply remove the intact analog flight stick from it housing and jury rig a mounting for it under my control panel, it should work fine. Then for the other joystick, I would hack the hat-switch on the flight stick(since the hat-switch is digital). This way, I would esentially create two separate joysticks from one, one analog flight stick and one digital joystick.
As far as having them control the same joystick, that does sound impossible. But why couldn't you just configure your flight stick games with the flight stick as the controller and use the other stick the rest of the time?
NoBonus