I'd recommend maybe switching to using the mouse instead emulating a light gun. While not really in theme because it's not too typical for NES games to utilize a zapper and controller at the same time it's still in the realm of NES.
We would consider just using the mouse (or having it as an option to turn it on/off) if we keep working on this. We tried staying within the given framework of the jam very strictly, as we aimed for authenticity (and to not be disqualified haha).