What hardware would I use to attached this tight to a wall?
I would fabricate or locate a a hanger with a single hole for the screw and a hanger loop.  Use your machine screw to mount the hanger loop to the plaque and hang it on a standard picture hanger suitable for your wall type.  You could swap to flush screws if it stuck out too much and put spacer shims on the sides in back if needed so it sits flat