I would cement a threaded rod in the spaces between the stones that align and sized to the holes in the address back board.

Yep, ^^^ use epoxy anchors, and them shim behind the sign to keep it flat.

I think the above methods could work. I'm just disappointed that no one mentioned duct tape as plan A.

Or Gorilla Glue!

What color duct tape?

Looks like I see a mounting hole at the top. Presumably one at the bottom. Maybe 2 at the bottom would be better for stability in windy conditions. Use a level to determine where you need to shim. Top or bottom. Or both if shimming for level is hindered by the bolts.

@Mark Bischak, Architect,

Back in the good old days duct tape came in only one color, but now it's complicated. Now you need a color consultant to accompany you to the hardware store to buy duct tape. I'm partial to camouflage (it goes with everything,) but my wife will tell you to never let me pick colors or wallpaper.

^ not only colors, but you've probably seen the "duck" tape for sale which adds to the confusion

When the kids were little they actually made purses completely out of duct tape - pink and paisley purple.

I know. I had to get a bigger tool box just to include all the different colors. I am glad five pound sledge hammers come in limited colors.

@Mark Bischak, Architect,

You should consider adding the metric set of sledge hammers. Somehow a weight denominated in "kilos" seems more appropriate for a demolition tool.