I must say it has been fun watching all the hairsplitting on this. I have great respect for all the helpful commentators here, but there is a vast experience gap.
These medallions are old hat to me. I have bought, sold, and installed them for years and have had to duplicate existing several times due to original suppliers specific designs being no longer available.
I would hope that you have checked at least some of the many suppliers of pre-manufactured ones to see if the one needed is more readily available.
If you HAVE to make it solid or layered foam is the way to go for a couple reasons. One of the main ones is since it is light it is also very easy to install. Good quality construction adhesive and caulk for the edges and a prop while it dries does the trick. It machines easy and can be easily smoothed and painted. Yes, as Brady points out, HDU sign foam is superior (more dense) than the "denser" and much cheaper insulation foam, but they both machine just fine for this type of project. I liked a 1/2" ball nose with 10% stepover. My first shot at it was based on the experience of a really great signmaker and she used tons of the pink stuff for large installations. It worked like a charm so I became a believer. Worst part, like mdf, is cleaning up the cutting dust. light scraping/sanding took care of anything that needed it and sealing with shellac, as I mentioned before, or KILS gave a fine base coat for final paint. If you don't want to come back and remove the temp prop after install and the customer chokes you can also use a couple large flathead screws into a joist and immediately spackle them. There are several easy ways to skin this cat and when you actually do it you'll end up going "Why did I worry about it so much?"