The passenger side register is very difficult to remove without breaking. I would recommend leaving out the bolt that goes behind it when re-installing the dashpad that way you don't have to worry about it in future dashpad removals.
Once you have the HVAC control panel out you'll be able to see if the cable is bent. It should be straight with only a deliberate manufactured shape to engage the levers. It should slide freely inside the blue cable sleeving. Without seeing it, I can't say for sure the cause of the wobbly lever. It's all snap together so it shouldn't really wobble. Tight is fairly normal on an unserviced HVAC control panel. I cleaned the cables with brake parts cleaner, then lubed them all with either silicone spray or maybe WD-40. It's been a while so I don't remember for sure but either would probably work.
Thank you!!
From what I can see with the HVAC control panel off, the cable looks as you described, straight with only a deliberate manufactured shape, but I'll (try to) take more of the dash apart so I can better see the cable and lever, and also if something else is bent or broken.
