I love the challenge of spatial problems like this one. While working for a sign company, we were faced with executing an idea by a design firm. It looked like this:

The monument sign was not a problem, but the dimensional plaque was outside the areas of expertise of my employer at the time. At the time, I was involved in a CNC hobby, and suggested we carve the logo plaque out of HDU foam. HDU foam is very stable, machines easily, and can be finished to simulate many materials, including the statuary brass specified for this project.
Based on the 2D image, I created a domed 3D model of the plaque. This is not some kind of software feature, mind you, but a time-consuming task that required many skills akin to sculpting.
I was able to export this three-dimensional model and import it into the CNC software. Here, I produced three-dimensional toolpaths. The series of photos below show the machining progress as material is routed away from the HDU block.
And this is the final piece, before hand finishing: