Well, then, have a real Church wedding.
This changes nothing in that regard. In the eyes of the Church, you are married with the real Church wedding.
You can consider going to the JP just a licensing thing. To get the State to acknowledge what has already happened in truth.
You married Mark?
If if was good enough for you - why are you changing it for us?
Why isn’t it good enough that we get the *exact* same thing you had?