Thanks for getting back to me! So in your case, you just attached that Moment Mount directly onto a ProClip Car Base and not to the
Actual MagSafe Mount that they have.
Like you, I also use Wired CarPlay. When ProClip released that MagSafe Mount, I wanted one but tried to avoid having to buy an actual MagSage Puck to put in it when I didn't actually need it for charging. I tried to find a magnet of the exact size as the official MagSafe puck so I could put it on there and not have to buy a $39 Magsafe charger, but I could never find anything with the right dimensions. I even came across the very same Moment mount you are using and thought it might work, but found out it's too big to fit in the ProClip holder.
Ultimately, I did just buy a MagSafe Charger, cut off the cord and stuck it in the ProClip. An expensive solution, but one I am quite happy with at least.