"How were these things originally mounted?"

Without a junction box.

This has not been allowed for a LONG time.

What about a handy/gem box? It looks big enough to cover a single gang box. I am still unclear as to how it would be mounted to the box (I've asked the seller for more information and am awaiting a response). The first thing that comes to mind is a swivel crossbar, but I've only ever seen those in 4" sizes.

" I am still unclear as to how it would be mounted to the box"

They do not actually have to attach\h to the box, just cover it and be solidly mounted.

Mounting to the wall is fine, as long as the box and any wiring compartment on the back are covered.

If the wiring compartment is large than the box you may need to cover the excess with metal, but most AHJs are not going to look all that hard (and plaster and drywall are NOT considered flammable surfaces).
One 'trick' to wiring volume is to use a larger 4x4 box with a single gang plaster ring.
Now you have a single gang opening but the larger box volume.