You don't need any carabiner or other complicated solutions....
Seems like you need my " IDD " system
Inverted Donkey Dick....
You only need a one end spliced spectra rope (i.e. = you can use some old pigtail ) and a piece of PU tube ....
Since i ride with Dakine harness i attach the IDD to the bridge of the hook , but i also used it with other harnesses in the past attaching it to the center of the spreader bar just make a large tube ....
Remove the original donkey dick from your CL ...and ready
I use this system for many years now ,and never have a problem.... ,you have completly freedom of your CL rotating sideways in your hook ...
Carabiners , Rings, and others tends to deform and tear apart your CL in no time, since all the load of the kite it's at one narrow point in the middle of the CL ...