Joined: Sep 2012
Location: Sydney Australia
As you don't see the sheet metal under the mirror, I would use a thin blade screwdriver and with a hammer, tap from the outside edge of the hole inwards. This makes the hole smaller with a bur that would make the screw fit once again.
Or the above comment sounds like a good idea but make sure the gauge of the screw is larger but the head is the same as the old one.
15/5/1964 260 Manual Coupe.
23/3/1965 289 Manual Fastback.