My mirrors have a lip that slides under the rubber on 2 sides and then usees 2 sided tape on the back vertical edge to keep the mirror from moving. The rubber holds the mirror tight.
Now in your case, you can cut a piece of thin sheet metal a bit larger on the bottom and top angle, attach it to the mirror back with flat head counter sunk screws, and slip the sheet metal under the rubber. Put the 2 sided tape on the back edge and pull the protective film off once the mirror is in place. I'll put additional pics on later today with a detailed explanation.