Many thanks for your support.
I tried a lot of things because of the second fire button. Since a lot of people tend to hold the fire button down all the time and accidentally pull the joystick down very quickly, simply pushing the joystick down while firing was not an option. Therefore you have to pull the joystick down without the fire button and then press the button while the stick is still being pulled down. Of course, this has the disadvantage that in the heat of the moment you sometimes can't do this fast enough.
A second button on the joystick would be fantastic, but unfortunately I don't know of any standardized design that I could support.