Read the instructions that came with the light. They will tell you the type of electrical box to which the light can be attached.

IMO:

• Buy a light that will attach to the existing electrical box.
• Buy dark-sky compliant outdoor lights that illuminate only the areas that need it.

This light is neither.

I know you don't want to send these back, but I think they are going to be very problematic for the stone. They simply won't lay flat without filling in the space somehow or chiseling out stone. Send them back. Go to a lighting store where a real person who is knowledgeable can offer suggestions on a light that will work. The lights are lovely but they aren't unique. I'm sure a lighting professional can quickly find a large light very much like this one but with a base that will fit the existing. And I have found that all retail lighting stores will match or beat online prices.

According to the specifications, that light's "Backplate covers a standard 4” hexagonal recessed outlet box". The problem is that the stone above and below the electrical box will block the 9" high backplate.

I was afraid this is what I may hear! Yes, I think I may end up sending them back. Lesson learned as it will probably include a restocking fee from Progress Lighting. Thank you for the explanation behind your answers...that is really helpful. Also, appreciate the recommendations on moving forward!

you can by on amazon a wooden mounting block for exactly this. core foam might also work.

https://www.lowes.com/pd/Builders-Edge-5-in-x-6-75-in-Clay-Vinyl-Universal-Mounting-Block/3046048