What to do...remote mirror mounting?

I see what you mean. IMO, your choices are Bondo, lead, or patch panel. If you use Bondo or lead, do fill the holes you need to use. If you use a patch panel, make a template that has the size and location of the needed holes in relation to the rest of the door. For example: Use the front window track where it disappears into the door as the reference point for your template. Failing to do this gives you the holes in the right place for the mirror, but not for the right place on the door.

It goes without saying, use any of these three methods, and the area needs to be repainted.