The Z-Rod is moving freely - How shall I attempt to fix it?

So after one day of not using the printer, I noticed an extreme imbalance, I think the imbalance might be the cause of the rod issue, or the rod issue caused the imbalance

Sending an +10 X command, the Z was also moving extremely upwards, the Y commands were being ignored etc. I'm guessing the autolevel logic was extremely off, which might have caused all of this (commands are from the MatterControl UI)

Then I've noticed the Z imbalance, and the rod issue

The rod is free, inspecting the rod, I'm guessing I need to free (loosen the screw) the clamp's upper part that fixes the rod, then re-apply some glue to the rod, and clamp it back in, without opening the printer, or removing the clamp (the thing that wobbles, keeps the rod, transfers the movement to the rod)

Am I correct?

The clamp is already tightened at the current state, however the white coating of the rod has been lost it's grip, which is a challenge I guess, the white coating seems to be the component that generates the grip

(I've also inspected the forum a bit, you can't search for "rod"/"z rod", however a previous advice was to fasten the screw, doesn't apply to my case I guess, since it's already fastened)

 

Well I think gluing it was a bad idea, it's something that should be easily removable, it seems

I've removed it, put some thin painters tape around the part to be gripped (tried insulation tape, to replace the worn out teflon tape, was too thick), and screwed it back in, seems stable now, might even be better than before

The left rod used to wobble, now the right one wobbles (the right one was the one I removed and re-screwed)

It also doesn't lean to the middle of the rod-holder plastic construct ( the part where holds the 2 extruder rods and 2 Z rods )
While the left one is aligned in the middle, this new one is close to one side, I'm unsure whether it's an issue or not

The wobble isn't extreme