Here's a thought: given that the site already uses PAM, perhaps they could add a PAM process to monitor the inbox that Maileater is currently configured for, and point Maileater at a new inbox. The PAM process would inspect each incoming email. If the email refers to a Closed ticket, strip out the ticket reference and send the updated email to the new Maileater inbox, where it should cause a new ticket to be raised. Otherwise, forward the email to the new Maileater inbox without alteration, where it will update the ticket.
There may be a touch of the 'Heath Robinson' about this, but I'm sure it would work...