Hanging a mirror from its wooden frame
I am at a loss as to what "some kind of "platform", sort-of like the one pictured below " is supposed to do or how it would be used.

I would Use a french cleat and some stand offs on the bottom of equal thickness of the cleat so the mirror hangs parallel to the wall. ( Or adjust the thickness of the standoff to achieve any angle you like ) 

Another option is to use two D-rings on the back of the mirror with a cable and one or two solid (in structure or toggle anchors) hangers on the wall.  This system is common for heavy mirrors and photographs .  



Or another option would be to use Keyhole mounting brackets 

The advantage of the D-rings and cable is that you can adjust the mirror to hang straight after it is mounted, but with the cleat and keyhole care must be taken to mount the mirror LEVEL. The D-ring is a more  adjustable system, and the cleat and keyhole are more solid mounts, because the mirror cannot move around—even if bumped slightly—after it is installed.