Nice that you made some significant progress @DaleKramer!
As you added an elastic support to the lower surface of the coin, it actually does not deform symmetrically and the lower surface remains almost undeformed. I would probably use either both surfaces or the side face - btw. you can also use an orthotropic elastic support stiffness, and for example put a close to zero value in normal direction.
Wrt the small deformation limitation I would say in your case it should be fine as the normals of the cyclic symmetry plane do not change.
Your coin is also smaller than expected as you got some (relative to the final thickness) large contact penetration. You can try to increase the penalty factor or switch to a lagrangian contact to reduce the contact penetration.
Best,
Richard