Here's how I fixed it (I think).
I found a picture online of a dashboard with the mounts still in tact. This was my "guide" for what the dash should look like.
The mount on the left side of my dash was almost completely gone.
The mount on the right side was missing the middle section.
I used hard plastic (happened to be an old Radio Shack project box) that I had sitting around and used a dremel to replicate the missing or damaged pieces as best I could.
The metal clips are available from LMR. I got mine as part of the interior screw kit, not sure if they sell them individually. They are on the dash from the factory and are necessary if you want to be able to screw the the bezel down. The same kit also includes the correct bezel screws for these mounts. Again, not sure if they're available indivudually.
I used 3M 4475 Industrial Plastic Adhesive to glue the new mounts to the dash.
It seems to be rock solid. I had explored a bunch of options before going this route, including fiberglass, epoxy, JB Weld. I chose this way because I couldn't get anything to adhere to the plastic as well as this did. I hope it works in the long run--for now it doesn't seem to be going anywhere.