Cracked chrome bezel around display

I dropped my phone a while ago, and noticed some cracks in the small chrome bezel around the display. Not really a problem until recently... when a couple of the cracks near the corner allowed part of the bezel to fall off. I've been keeping the piece in place with superglue and tape, but it's not really a long term solution.

Looking at the guides and teardown, it appears that the only way to replace the chrome bezel is to replace the whole display and digitizer assembly. Is this true? The display has no problems, so I hesitate to spend $200+ for a little piece of chrome. Do you have any other suggestions to keep the pieces in place?