I have the same issue with my original rear-view mirror, so I'm curious as to the advice offered as well. For regular use, I have a newer, larger, more convex mirror that clips over the original. But when I show the car, I remove it.
On a related note, I understand that inexpensive, stick-on mirrored tiles from home-improvement stores make good replacements for the rear seat vanity mirrors. I don't plan to find out first-hand until I'm ready to send out the wood trim for refinishing. Has anyone here tried that?