Yes, this happens a lot (not quite as embarrassing as this one but still), despite having changed the footer the way you suggested. People just don’t see it. I think you have pinpointed the core of the issue here:
I wonder if it might help to have a site setting that allows admins to change the sender name from the poster (user)name to the name of the forum (perhaps "on behalf of poster) or something. That way it should be quite clear in any email client that a reply to that email will go to the forum.
We’d not be loosing much because the posters name (and avatar!) is still included in the email body.