As an update to this thread you might find this a good place to inject received by dates into your stream. It looks like you will lose some of the associated metadata such as read/unread status, if it was sent by you, etc.... but as a first pass approximation this should work well.
[SOLVED] Using zmlmtpinject
There may be a sql command that you could run to update the flags in the mail_item table to reflect when something is sent by the owner of the mailbox to mark it as being a sent item but I don't know the flag structure or if that is how they track sent status.