Thanks, Ray; I've been thinking along the same lines re: dropping the backup MX.
As for the accepted emails, my SME is configured to use an "Internal mail server", so my "goodrcptto" includes "@mydomain.org", allowing receipt of all incoming email. Perhaps this is the problem!
I don't supposed there's an LDAP module for qpsmtpd that integrates with the goodrcptto plugin, or a plugin that monitors the qmail logs for email declined by my internal mail server, and adds those addresses to 'badrcptto', or something like that?