Updating shared ref from remote helper, or fetch hook

I'm working on an hg remote helper that uses git notes for the sha1 revision, so that git users can more easily refer to specific commits when communicating with hg users. Since there may be multiple concurrent fast-import streams, I write the notes to a private ref (refs/notes/hg-REMOTE), to be merged eventually using

  git notes --ref hg merge hg-REMOTE*

There will never be conflicts because each hg commit translates to a unique git commit, thus even if multiple concurrent remotes process the same commit, the corresponding note will match.

Unfortunately, I couldn't find a safe way to get this run after a fetch or clone. Of course I can ask the user to arrange to have this command run, but it would be a better interface to have it run automatically since it is a natural responsibility of the remote helper. Am I missing a way to do this or a viable alternative approach?