My very first (and maybe last) Thing. Credits go out to Dafft for all his advice and the template for my Thing. I rebuilt the wall mount from scratch, replaced the circular holes for the nuts with hexagonal ones, and left out the indentations for the wall screws.
Take two M4 nuts and put them in the freezer. After 10 minutes, they should be cold enough to perfectly fit into the corresponding hexagonal holes. Add super glue if necessary. From the reverse, screw two M4 screws (e. g., M4x12) in until they line up perfectly with the nuts. Secure with super glue or two-component adhesive. Mount to the wall using wall plugs and screws or double-sided adhesive tape.