Surface Doming Generation

Problem:
I am attempting to create a rounded or domed surface from closed curves and/or ones that intersect. The end goal is correct surface shapes to create a die to coin this on a small copper blank. The intermediate goal is to 3D print
the coins. The first effort was a very complex coin. So the next two have been greatly simplified. Attached is a simple one. Once the process is understood the complex one will only take more time.

Attempts:
Heightfield was a solution I saw on the forum and although that does fascinating things, I could not see how to use the results. To use Heightfield, I rendered the curves as a .jpg then used that image. I also have MecSoft Art which is
supposed to do this but the results are not clean at the intersection of the curves and the base surface. It has been a while but I tried Patch and Brep and just watched the Displacement tutorial by Brian James. It appears Displacement requires a texture map. I will play with that tomorrow.

Extruding the curves works for a casting but not for coining. The images need to be 3D but smoothly connect to the base surface.

This can’t be rocket science but I seem to be making it so.

Three files attached. One is an example…Sunshine Silver
One is the Rhino file of the coin to have surfaces created from curves. And the third is the quail created in RhinoART.

Request:
Thanks for any ideas you have to get a slightly domed surface (full height will be approx. 0.008 inches) for the text, quail, and between the 2
circles.

Quail Studio Logo.3dm (390.6 KB)Quail_RhinoART Mesh.3dm (7.0 MB)