I have time for typing now, but I'm on a phone, so I can't make pictures(easily). We'll start from the start. You have...
plaster wall
marble mantle with a glass plate on top
First, I'm assuming you have room to lean a mirror on the mantle. It's deep enough to keep the mirror from toppling, even if the base is secure, right? If not, you'll need a top anchor, but it won't have to hold the full mirror weight. Just enough to keep it from falling away from the wall.
Main goal... Keep the bottom of the mirror from sliding away from the wall.
I imagine the glass has a gap of some width at the wall. If there's zero gap, then my idea won't work. The idea is to stick something between the glass and wall(not shown in my pic above, but it's where the strings are going at the top) that'll hold firmly as a wedge using friction. A nail if the gap is wide, or something like a knife blade(cut a chunk off a crappy table knife) if it's narrow. Attach a string to that, then tie the other end of the string to the mirror. Result = bottom of mirror can't go farther from the wall than the string will allow. The wedge you made between the glass and wall will hold it in place.
Potential problems...
You get carried away tapping the wedge in place, and break the glass.
Tapping the wedge in breaks the epoxy bond, and the glass comes loose from the marble.
You loosen the epoxy, but don't notice, and weight of the mirror slooowly pushes the glass away from the wall, your anchor comes loose, and the mirror falls.
As noted above, if the angle of the leaning mirror is too steep, it could topple from the top, so that'll have to be accounted for.