For such question specific to mesh orders for structure, it is better to have a new, dedicated post. Please do write a new post next when your question is not exactly the same as the origial post.
From what you described, the overlaps happen among the polysterene sphere, au coating sphere and a gold thin film.
Obviously the gold thin film should not have the highest mesh order.The polysterene sphere should. The au-coating shphere should have lower mesh order since it has to keep the polysterene sphere well. Regard to the substrate, if any of the above mentioned 3 geometries penetrates into it, the substrate should have the most-highest mesh order, as the sphere does not penetrate in experiment.
In mesh order, the small the number, the higher the priority. Thus from my experience in the lab, I recommend the following:
substrate, the default mesh order 2;
polysterene sphere, mesh order 3;
au-coating sphere, mesh order 4.
gold thin film, mesh order 4;
Depending on the process techniques, you may change them.
Usually the polysterene sphere may not well maintain its spehre shape on the substrate by the process. It can be cut a little by the substrate, or by another residual material in the process.
Please use index monitor to check the resulting index profile.