Before I switched to iRedMail, I used script run from cron on the email server for over-the-quota notifications - same scenario could be used to your purpose.
It checked the quotas for all users and wrote the email directly in the maildir, so bypassing all the quota processing/checks.
Not ideal solution, but it worked.
Note:
- quota gets out of sync with this write (but I could live with it as the notification emails are usually tiny),
- you should prevent spamming the user with the email (remember, email was already sent / I used special file suffix),
- not sure, if dovecot will work correctly (moving from new to cur could fail when over quota - I used it on dovecot 1.x, so don't know this).