well, just remember that these joys are not built to handle extreme stress - esp on the z rotation.
Popping a gun on the shaft would add weight to it, and also, would provide extra leverage. (like a 't' wrench) These factors may lead to ripping the mechanism completely appart with a single excited left to right swing.
i had a simular problem with the first analog joy i tried for a sinistar mod. The rubber x i made was too strong for the plastic joints, and ripped it appart. Tried strong cableties arrond the assembly - but still not good enough to handle the extreme stresses.