Ballmount bracket predicament

The bottom of this ballmount can rotate.

The bracket is attached with a screw to the bottom of the ballmount and requires rotation to unscrew.

The screw is so tight that, even with the ballmount rotation locked, it still just rotates the ballmount.

I can't clamp the sides of the ballmount bottom as it is too fragile.

Surely I am not the first person in the world to have this problem. Is there a trick to getting this loose?

I tried leaving it in the fridge, hoping it would shrink enough to come loose or something but no dice.

Thank you for your time, feel free to laugh at me.