I’m at the same stage as you are!
I printed the 13mm Z nut lock, as I’m using metric hardware, so an 8mm Z Axis screw.
I found that the coupler nut slid down to the bottom, and the clamp gap opened slightly, about .5mm.
Therefore I do not see the problem you are having.
But this coupler nut should not move, as you would loose all Z tolerance if it did!
I checked across the flats on my coupler nut, and it measures about 13.1mm.