If you don't want to spend any money on this, you need to resort to means offered by the mail platforms used. GMail is the odd one out, I'm afraid there's no 'automated' process offered out of the box except for following strict manual procedures. If it's a one-way sync, you could develop something yourself, eg clear the overview calendar, and import/merge the source calendars using imap (as GMail doesn't support EWS).