Tristan, I agree with those that mentioned that the screw driver has slipped and wedged between the rod and the casting. Looking at your top photo, it appears that the screw driver is centered and the cast top link is up on that end hinting that the screw driver tip has slipped off and wedged the rod. Do you have a slide hammer? If so, you could try to clamp one end to the screw driver and drive (pull) the screw driver back out. Might be a good idea to do Kendell's suggestion of removing the screwdriver handle and bend the shank into a hook.
<font size="+2">SLIDE HAMMER</font>
<font size="+2">SLIDE HAMMER</font>