This isn't the complete answer to your problem, but one of the puzzle pieces that might help your situation.
smtpd_recipient_restrictions = reject_non_fqdn_sender http://www.postfix.org/postconf.5.html#reject_non_fqdn_sender
We have received a big batch of phishing emails that was not properly detected (hence not blocked). They all shared a special characteristic: To: Recipients From: Administrateur Reply-To: <nore...@admin.fr> Return-Path: <> To and From are not qualified email addresses, Reply-To is bogus but qualified even though admin.fr does not have an MX record. Envelope Mail From / Return-Path is blank. Is there a proper way to block this kind of junk in Postfix or do I have to rely on my antispam (that will need tuning, obviously)?