I believe fancy joystick key binders (such as the Saitek one) will work by intercepting the joystick button events (e.g., replacing 'trigger press' with 'space bar'), but less fancy ones (like joy2key) don't do this (they say 'trigger press' as well as 'space bar'). I noticed when testing that this resulted in e.g., when attempting to fire rockets with a salvo of 1, two rockets being fired: one from the built-in joystick trigger event, and one from joy2key seeing the trigger press and simulating a spacebar (fire weapon) keypress.

In any case, I've just finished (bar a little more testing) a mod which will add the behaviour I want. I'd like to eventually have fully remappable controls in-game but I have exams coming up so this is probably all I'll get done for a little while.