When you say tighten one screw from behind. Is it just threaded nut and screw/bolt that goes through the side wall?
Mine are lag screw/bolts from mirror side. A block of wood is captured/molded in fiberglass. I was able to get some lag screws the went deeper but not through the glass on cap.
Owners have nut and bolted through the wall.... BUT someone pointed out the mirrors are no longer break away and would do a lot more damage if caught ,it happens as they protrude out.
The repair of these wooden holes fall into the marine world for solutions. They make specific wood hardening chemicals and epoxies but are very thin. I seen looked into marine based options to repair holes mixed with chopped glass , sawdust or plugs. West Systems is a high standard of marine epoxies with lots of info and solution to problems on website. West Systems is also very popular with hobbyist.
I considered a fiberglass hollow tube epoxied into hole. I wonder if best to pre split or score it like a drywall anchor , so it would be less likely spin out in the hole and expand easier. Also considered threaded studs and female machine threaded plugs in the holes.
A company or machinist should create a really long "soft wood threaded insert" to repair these.
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