Given the complete lack of dead zone in the middle, you're going to have a hell of a time centering that spaceship of yours, and since you can't remap the left stick at all, there's really nothing that can be done about it.
So if the game interprets the start button as Joystick button 8, which the game has mapped to full throttle but I have mapped to shields, it'll perform both actions. I find using your wingmen really helps to make both of these games a lot easier.