Somebody had apparently tried to pry the radio bezel off the wrong way. So I picked up the radio removal tools, popped the radio out, and pulled the bezel correctly. Sure enough, both fasteners on the right side had been busted off.
So I rummaged around and found a plastic rod (from an old hanging plastic planter), cut a couple of short pieces, filled the hole in the old mounting peg with superglue, and mounted the fasteners via the rods.
Let it dry for an hour or two and reassembled. So far it looks great. Hopefully the glue joints won't bust loose from vibration. Time will tell. Here's a link to the pics.