so here's the worklog of a new stick. It starts of course with the case.
No screws so far. Only pins and glue.
Middle plate. I drilled holes at the four corners for the screws. To sink the screw nuts the hole is slighty wider at the top.
With this technique no screws holes disturbs the plexi. Additionally only 4 screws are needed for the whole case.
Countersink close up.