The disks are indeed optical surfaces (mirrors). They have a large (10m) radius of curvature, which I ignored for now for simplicity.
Typically the whole thing sits on 4 symmetrically placed rubbery balls or on rounded pins on springs, which are meant to add a little bit of vibration isolation. It's not rigidly attached to the supports, though, it just sits on them, so I'm not sure what is the most realistic type of support to use that would constrain its xz motion. The contact surface is supposed to be just the very small areas at the center of those holes where the flat and rounded surfaces intersect.
I can see how supporting individual nodes is problematic and a finite area is the way to go. Maybe to get rid of the dependence on the surface area a better approach would be to redo the simulation with several different contact sizes and try to extrapolate to zero?